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Problem-Solving Strategies and Obstacles
Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.
What Is Problem-Solving?
In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.
A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.
Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.
The problem-solving process involves:
- Discovery of the problem
- Deciding to tackle the issue
- Seeking to understand the problem more fully
- Researching available options or solutions
- Taking action to resolve the issue
Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.
Problem-Solving Mental Processes
Several mental processes are at work during problem-solving. Among them are:
- Perceptually recognizing the problem
- Representing the problem in memory
- Considering relevant information that applies to the problem
- Identifying different aspects of the problem
- Labeling and describing the problem
Problem-Solving Strategies
There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.
An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.
In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.
One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.
There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.
Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.
If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.
While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.
Trial and Error
A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.
This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.
In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.
Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .
Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.
How to Apply Problem-Solving Strategies in Real Life
If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:
- Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
- Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
- Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
- Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.
Obstacles to Problem-Solving
Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:
- Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
- Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
- Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
- Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.
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How to Improve Your Problem-Solving Skills
In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:
- Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
- Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
- Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
- Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
- Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
- Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.
You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.
Sarathy V. Real world problem-solving . Front Hum Neurosci . 2018;12:261. doi:10.3389/fnhum.2018.00261
Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20
Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9
Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579
Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517
Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7
Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality . Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050
Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition . Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568
National Alliance on Mental Illness. Warning signs and symptoms .
Mayer RE. Thinking, problem solving, cognition, 2nd ed .
Schooler JW, Ohlsson S, Brooks K. Thoughts beyond words: When language overshadows insight. J Experiment Psychol: General . 1993;122:166-183. doi:10.1037/0096-3445.2.166
By Kendra Cherry Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
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Although the method which one is going to use when solving a math problem depends on the exact issue in question, there are general steps and guidelines one can follow. This is the reason why so many students are looking for a math problem solver. Having it on hand will definitely speed up the whole process. Here are the strategies that might come in handy. Having familiarized yourself with these tips, you won’t even have to search for a free math problem solver.
The first step you need to take is to understand the problem. Begin with identifying the type of the problem and determine whether it is a fraction, a quadratic equation or a word problem. This is one of the most significant aspects even if you are searching for a math problem solver with steps as it helps you figure out what you are supposed to do. The next step is to read the problem carefully and don’t attempt to solve it right away. If you realize that it’s too complex, find an online math problem solver to get qualified assistance with your assignment. What is vital to mention is that sometimes it takes time to figure out how to best approach the task at hand. Then, try to create a visual representation of the problem to better understand how to deal with it. Drawing a problem is a smarter choice than looking for a free math problem solver as you acquire new skills as well as complete your assignment on your own. Another great tip is to look for patterns when you are reviewing your problem and the available information. The reason why these patterns are important is because finding them will lead to the needed math problem solver you’ve been looking for all this time.
Having gathered all the information you need, it’s time to get down to developing a plan on how you are going to deal with your issue without using a free math problem solver. If you are in need of a math problem solver with steps, what you need to do next is figure out the formulas you’re going to use to complete your math assignment. Then, write down a step-by-step guide on all the things you are supposed to do to solve your problem and start working on it to get the correct answer. This process may be time-consuming as you need to double-check that the method you have chosen is the right one. While you are solving the problem, try to look for alternatives in order to check all the possible variants. Ask for help from an online math problem solver if necessary. Compare the answers you got to your estimates. When you are done, allocate some time to reflect on the problem, as well as make sure you have chosen the correct solution. Solving a math problem sometimes takes more time and effort. Yet, you’ll be really pleased when you manage to complete such an assignment on your own.
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V ice President Kamala Harris is a difficult problem for President Joe Biden to solve. Her poll ratings are weak, and her job performance has been a big disappointment to many Democrats . Stories about her lack of preparation and office mismanagement are already legend. Her inability, or, perhaps, refusal, to tackle complex issues when she had the chance, such as border security and immigration reform, has been an embarrassment.
If Biden runs again, he’ll be 82 soon after the election. His age would make his vice presidential pick that much more important. Even though he’s likely to keep Harris on the ticket, Democratic operatives are increasingly concerned about how voters will react to her remaining a heartbeat away from the presidency for another four years. There’s nothing new about vice presidents being political liabilities, or getting dumped at reelection time. Replacing a running mate, nevertheless, is a delicate matter.
KAMALA HARRIS FINDS HERSELF BACK IN A FAMILIAR PLACE: TIED TO THE SENATE
Aaron Burr, who ran for vice president with Thomas Jefferson in 1800, secretly tried to get the Electoral College to elect him president instead. Four years later, Jefferson barred Burr from the ticket and later ordered his arrest as a traitor.
Abraham Lincoln rarely saw his vice president, Hannibal Hamlin, who oddly served as a guard and company cook during the last part of the Civil War. He was replaced on the ticket in 1864 by Andrew Johnson, who became president when Lincoln was assassinated less than six weeks into the new term.
Ulysses Grant’s first vice president was implicated in a scandal and defeated for renomination. Grover Cleveland ran three times for president, winning twice. In each race, he had a different running mate.
Franklin Roosevelt’s selection of House Speaker John Nance Garner as vice president was the result of a deal for delegates at the 1932 Democratic convention. Never close to Roosevelt, Garner stayed on the ticket in 1936 but was shown the door in 1940 when Henry Wallace, the agriculture secretary, replaced him.
In 1944, a gravely ill Roosevelt sought a fourth term. Democratic bosses feared that Wallace, a left-wing mystic, would succeed to the presidency if he remained vice president. The wily FDR secretly allowed party leaders to sideline Wallace, throwing open the vice presidential nomination at the convention. The prize went to Sen. Harry Truman. After only 10 weeks as vice president, Truman became president when Roosevelt died.
The last vice president to be excluded from the ticket was Nelson Rockefeller in 1976. When Gerald Ford became president upon Richard Nixon’s resignation, he appointed the former New York governor to fill the second spot. But after a strong challenge from Ronald Reagan in GOP primaries, Ford needed to strengthen his right flank. He couldn’t do it with Rockefeller, a centrist. A hard-bitten realist, Rockefeller understood the game. He graciously offered to withdraw, and Ford accepted.
Would Harris step aside, as Rockefeller did? Would she do it to keep former President Donald Trump or Gov. Ron DeSantis (R-FL) from winning? It’s unlikely. First, her historic role as the nation’s first woman, African American, and Asian American vice president would make doing so more complicated. Second, Harris still wants to be president.
If Biden doesn’t run again, Harris likely will. But if her next presidential campaign is anything like the last one, she’d have an uphill climb. When Harris started her 2020 White House bid, pundits thought she had great potential. After spending $42 million, she dropped out before any votes were cast. Polls showed she lacked support from key constituencies, particularly women and black voters.
Democrats rightly fear that Harris, if she becomes their presidential nominee in 2024, would lose to either Trump or DeSantis. That makes her a problem for both Biden and the party. But at some point, they need to figure out, as the Sound of Music song ponders, "How do you keep a wave upon the sand?"
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Ron Faucheux is a nonpartisan political analyst, pollster, and writer. He publishes LunchtimePolitics.com , a nationwide newsletter on polls and public opinion.
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How to Solve a Problem
Last Updated: December 20, 2022 References Approved
This article was co-authored by Rachel Clissold . Rachel Clissold is a Life Coach and Consultant in Sydney, Australia. With over six years of coaching experience and over 17 years of corporate training, Rachel specializes in helping business leaders move through internal roadblocks, gain more freedom and clarity, and optimize their company’s efficiency and productivity. Rachel uses a wide range of techniques including coaching, intuitive guidance, neuro-linguistic programming, and holistic biohacking to help clients overcome fear, break through limitations, and bring their epic visions to life. Rachel is an acclaimed Reiki Master Practitioner, Qualified practitioner in NLP, EFT, Hypnosis & Past Life Regression. She has created events with up to 500 people around Australia, United Kingdom, Bali, and Costa Rica. There are 12 references cited in this article, which can be found at the bottom of the page. wikiHow marks an article as reader-approved once it receives enough positive feedback. This article received 14 testimonials and 91% of readers who voted found it helpful, earning it our reader-approved status. This article has been viewed 1,277,642 times.
How you deal with challenges will often determine your success and happiness. If you’re stuck on how to solve a problem, try defining it and breaking it into smaller pieces. Choose whether to approach the problem logically or whether you should think about how the outcome might make you feel. Find ways to creatively approach your problems by working with other people and approaching the problem from a different perspective.
Approaching the Problem
- For example, if your room is constantly messy, the problem might not be that you’re a messy person. It might be that you lack containers or places to put your items in an organized way.
- Try to be as clear and thorough as possible when defining the problem. If it is a personal issue, be honest with yourself as to the causes of the problem. If it is a logistics problem, determine exactly where and when the problem occurs.
- Determine whether the problem is real or self-created. Do you need to solve this problem or is this about something you want? Putting things in perspective can help you navigate the problem-solving process.
- For example, you might have several problems to solve and need to decide which ones to tackle first. Solving one problem may ease tension or take stress off of another problem.
- Once you make a decision, don’t doubt yourself. Be willing to look forward from that point on without wondering what would have happened had you chosen something else.
- For example, if you need to turn in many assignments to pass a class, focus on how many you have to do and approach them one by one.
- Try to combine and solve problems together whenever possible. For example, if you're running out of time to study, try listening to a recorded lecture while walking to class or flip through note cards as you're waiting for dinner.
- For example, if you’re trying to pass a cumulative test, figure out what you already know and what you need to study for. Review everything you already know, then start learning more information from your notes, textbook, or other resources that may help you.
- Pay attention to know these scenarios make you feel.
- For example, if you have a deadline, you may skip cooking dinner or going to the gym so that you can give that time to your project.
- Cut down on unnecessary tasks whenever possible. For example, you might get your groceries delivered to you to save on shopping time. You can spend that time instead on other tasks.
Taking a Creative Approach
- If you’re making a complex decision, write down your alternatives. This way, you won’t forget any options and will be able to cross off any that aren’t plausible.
- For example, you might be hungry and need something to eat. Think about whether you want to cook food, get fast food, order takeout, or sit down at a restaurant.
- Problems like accepting the job across the country that offers good pay but takes you away from your family may require different ways of approach. Consider the logical solution, but also consider your thoughts, feelings, and the way the decision affects others.
- For example, if you’re buying a home and not sure how to make your final decision, talk to other homeowners about their thoughts or regrets about buying a home.
- For example, if you’re having financial difficulties, notice how your efforts are affecting the money coming in and the money you’re spending. If keeping a budget helps, keep with it. If using cash exclusively is a headache, try something else.
- Keep a journal where you record your progress, successes, and challenges. You can look at this for motivation when you are feeling discouraged.
Managing Your Emotions While Confronting Difficulties
- The first step is often the scariest. Try doing something small to start. For example, if you're trying to become more active, start going for daily walks.
- For example, if you’re overwhelmed by having a long to-do list, maybe the problems isn’t the list, but not saying “no” to things you can’t do.
- If you're feeling stressed, angry, or overwhelmed, you may be burned out. Make a list of things that cause stress or frustration. Try to cut down on these in the future. If you start feeling overwhelmed again, it may be a sign that you need to cut back.
- Find a therapist by calling your local mental health clinic or your insurance provider. You can also get a recommendation from a physician or friend.
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- If you start feeling overwhelmed or frustrated, take a breather. Realize that every problem has a solution, but sometimes you're so wrapped up in it that you can't see anything but the problem. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- Don't turn away from your problems. It will come back sooner or later and it will be more difficult to solve. Common sense can help to reduce the size of the problem. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
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- ↑ https://hbr.org/2017/06/how-you-define-the-problem-determines-whether-you-solve-it
- ↑ https://www.cuesta.edu/student/resources/ssc/study_guides/critical_thinking/106_think_decisions.html
- ↑ https://au.reachout.com/articles/a-step-by-step-guide-to-problem-solving
- ↑ Rachel Clissold. Certified Life Coach. Expert Interview. 26 August 2020.
- ↑ https://serc.carleton.edu/geoethics/Decision-Making
- ↑ https://www.psychologytoday.com/blog/positive-psychology-in-the-classroom/201303/visualize-the-good-and-the-bad
- ↑ https://www.britannica.com/topic/operations-research/Resource-allocation
- ↑ https://www.niu.edu/citl/resources/guides/instructional-guide/brainstorming.shtml
- ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
- ↑ https://www.collegetransfer.net/Home/ChangeSwitchTransfer/I-want-to/Earn-My-College-Degree/Overcoming-Obstacles
- ↑ https://psychcentral.com/lib/5-ways-to-solve-all-your-problems/
- ↑ https://www.apa.org/topics/psychotherapy/understanding
About This Article
To solve a problem, start by brainstorming and writing down any solutions you can think of. Then, go through your list of solutions and cross off any that aren't plausible. Once you know what realistic options you have, choose one of them that makes the most sense for your situation. If the solution is long or complex, try breaking it up into smaller, more manageable steps so you don't get overwhelmed. Then, focus on one step at a time until you've solved your problem. To learn how to manage your emotions when you're solving a particularly difficult problem, scroll down. Did this summary help you? Yes No
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How to Solve Problems
- Laura Amico
To bring the best ideas forward, teams must build psychological safety.
Teams today aren’t just asked to execute tasks: They’re called upon to solve problems. You’d think that many brains working together would mean better solutions, but the reality is that too often problem-solving teams fall victim to inefficiency, conflict, and cautious conclusions. The two charts below will help your team think about how to collaborate better and come up with the best solutions for the thorniest challenges.
First, think of the last time you had to solve a problem. Maybe it was a big one: A major trade route is blocked and your product is time sensitive and must make it to market on time. Maybe it was a small one: A traffic jam on your way to work means you’re going to be late for your first meeting of the day. Whatever the size of the impact, in solving your problem you moved through five stages, according to “ Why Groups Struggle to Solve Problems Together ,” by Al Pittampalli.
Pittampalli finds that most of us, when working individually, move through these stages intuitively. It’s different when you’re working in a team, however. You need to stop and identify these different stages to make sure the group is aligned. For example, while one colleague might join a problem-solving discussion ready to evaluate assumptions (Stage 3), another might still be defining the problem (Stage 1). By defining each stage of your problem-solving explicitly, you increase the odds of your team coming to better solutions more smoothly.
This problem-solving technique gains extra power when applied to Alison Reynold’s and David Lewis’ research on problem-solving teams. In their article, “ The Two Traits of the Best Problem-Solving Teams ,” they find that highly effective teams typically have a pair of common features: They are cognitively diverse and they are psychologically safe. They also exhibit an array of characteristics associated with learning and confidence; these teammates tend to be curious, experimental, and nurturing, for example.
As you and your colleagues consider these ideas, think about the last problem you had to solve as a team. First, map out what you remember from each step of your problem-solving. Were all of you on the same page at each stage? What aspects of the problem did you consider — or might you have missed — as a result? What can you do differently the next time you have a problem to solve? Second, ask where your team sees themselves on the chart. What kinds of behaviors could your team adopt to help you move into that top-right quadrant?
- Laura Amico is a senior editor at Harvard Business Review.
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Define and solve a problem by using Solver
Solver is a Microsoft Excel add-in program you can use for what-if analysis. Use Solver to find an optimal (maximum or minimum) value for a formula in one cell — called the objective cell — subject to constraints, or limits, on the values of other formula cells on a worksheet. Solver works with a group of cells, called decision variables or simply variable cells that are used in computing the formulas in the objective and constraint cells. Solver adjusts the values in the decision variable cells to satisfy the limits on constraint cells and produce the result you want for the objective cell.
Put simply, you can use Solver to determine the maximum or minimum value of one cell by changing other cells. For example, you can change the amount of your projected advertising budget and see the effect on your projected profit amount.
Note: Versions of Solver prior to Excel 2007 referred to the objective cell as the "target cell," and the decision variable cells as "changing cells" or "adjustable cells". Many improvements were made to the Solver add-in for Excel 2010, so if you're using Excel 2007 your experience will be slightly different.
Example of a Solver evaluation
In the following example, the level of advertising in each quarter affects the number of units sold, indirectly determining the amount of sales revenue, the associated expenses, and the profit. Solver can change the quarterly budgets for advertising (decision variable cells B5:C5), up to a total budget constraint of $20,000 (cell F5), until the total profit (objective cell F7) reaches the maximum possible amount. The values in the variable cells are used to calculate the profit for each quarter, so they are related to the formula objective cell F7, =SUM (Q1 Profit:Q2 Profit).
1. Variable cells
2. Constrained cell
3. Objective cell
After Solver runs, the new values are as follows.
Define and solve a problem
Note: If the Solver command or the Analysis group is not available, you need to activate the Solver add-in. See: How to activate the Solver add-in.
In the Set Objective box, enter a cell reference or name for the objective cell. The objective cell must contain a formula.
Do one of the following:
If you want the value of the objective cell to be as large as possible, click Max .
If you want the value of the objective cell to be as small as possible, click Min .
If you want the objective cell to be a certain value, click Value of , and then type the value in the box.
In the By Changing Variable Cells box, enter a name or reference for each decision variable cell range. Separate the non-adjacent references with commas. The variable cells must be related directly or indirectly to the objective cell. You can specify up to 200 variable cells.
In the Subject to the Constraints box, enter any constraints that you want to apply by doing the following:
In the Solver Parameters dialog box, click Add .
In the Cell Reference box, enter the cell reference or name of the cell range for which you want to constrain the value.
Click the relationship ( <= , = , >= , int , bin , or dif ) that you want between the referenced cell and the constraint.If you click int , integer appears in the Constraint box. If you click bin , binary appears in the Constraint box. If you click dif , alldifferent appears in the Constraint box.
If you choose <=, =, or >= for the relationship in the Constraint box, type a number, a cell reference or name, or a formula.
To accept the constraint and add another, click Add .
To accept the constraint and return to the Solver Parameter s dialog box, click OK . Note You can apply the int , bin , and dif relationships only in constraints on decision variable cells.
You can change or delete an existing constraint by doing the following:
In the Solver Parameters dialog box, click the constraint that you want to change or delete.
Click Change and then make your changes, or click Delete .
Click Solve and do one of the following:
To keep the solution values on the worksheet, in the Solver Results dialog box, click Keep Solver Solution .
To restore the original values before you clicked Solve , click Restore Original Values .
You can interrupt the solution process by pressing Esc. Excel recalculates the worksheet with the last values that are found for the decision variable cells.
To create a report that is based on your solution after Solver finds a solution, you can click a report type in the Reports box and then click OK . The report is created on a new worksheet in your workbook. If Solver doesn't find a solution, only certain reports or no reports are available.
To save your decision variable cell values as a scenario that you can display later, click Save Scenario in the Solver Results dialog box, and then type a name for the scenario in the Scenario Name box.
Step through Solver trial solutions
After you define a problem, click Options in the Solver Parameters dialog box.
In the Options dialog box, select the Show Iteration Results check box to see the values of each trial solution, and then click OK .
In the Solver Parameters dialog box, click Solve .
In the Show Trial Solution dialog box, do one of the following:
To stop the solution process and display the Solver Results dialog box, click Stop .
To continue the solution process and display the next trial solution, click Continue .
Change how Solver finds solutions
In the Solver Parameters dialog box, click Options .
Choose or enter values for any of the options on the All Methods , GRG Nonlinear , and Evolutionary tabs in the dialog box.
Save or load a problem model
In the Solver Parameters dialog box, click Load/Save .
Enter a cell range for the model area, and click either Save or Load .
When you save a model, enter the reference for the first cell of a vertical range of empty cells in which you want to place the problem model. When you load a model, enter the reference for the entire range of cells that contains the problem model.
Tip: You can save the last selections in the Solver Parameters dialog box with a worksheet by saving the workbook. Each worksheet in a workbook may have its own Solver selections, and all of them are saved. You can also define more than one problem for a worksheet by clicking Load/Save to save problems individually.
Solving methods used by Solver
You can choose any of the following three algorithms or solving methods in the Solver Parameters dialog box:
Generalized Reduced Gradient (GRG) Nonlinear Use for problems that are smooth nonlinear.
LP Simplex Use for problems that are linear.
Evolutionary Use for problems that are non-smooth.
Important: You should enable the Solver add-in first. For more information, see Load the Solver add-in .
In the following example, the level of advertising in each quarter affects the number of units sold, indirectly determining the amount of sales revenue, the associated expenses, and the profit. Solver can change the quarterly budgets for advertising (decision variable cells B5:C5), up to a total budget constraint of $20,000 (cell D5), until the total profit (objective cell D7) reaches the maximum possible amount. The values in the variable cells are used to calculate the profit for each quarter, so they are related to the formula objective cell D7, =SUM(Q1 Profit:Q2 Profit).
In Excel 2016 for Mac: Click Data > Solver .
In Excel for Mac 2011: Click the Data tab, under Analysis , click Solver .
In Set Objective , enter a cell reference or name for the objective cell.
Note: The objective cell must contain a formula.
In the By Changing Variable Cells box, enter a name or reference for each decision variable cell range. Separate the nonadjacent references with commas.
The variable cells must be related directly or indirectly to the objective cell. You can specify up to 200 variable cells.
In the Subject to the Constraints box, add any constraints that you want to apply.
To add a constraint, follow these steps:
On the <= relationship pop-up menu, select the relationship that you want between the referenced cell and the constraint.If you choose <= , = , or >= , in the Constraint box, type a number, a cell reference or name, or a formula.
Note: You can only apply the int, bin, and dif relationships in constraints on decision variable cells.
Click Solve , and then do one of the following:
To interrupt the solution process, press ESC . Excel recalculates the sheet with the last values that are found for the adjustable cells.
To create a report that is based on your solution after Solver finds a solution, you can click a report type in the Reports box and then click OK . The report is created on a new sheet in your workbook. If Solver doesn't find a solution, the option to create a report is unavailable.
To save your adjusting cell values as a scenario that you can display later, click Save Scenario in the Solver Results dialog box, and then type a name for the scenario in the Scenario Name box.
After you define a problem, in the Solver Parameters dialog box, click Options .
Select the Show Iteration Results check box to see the values of each trial solution, and then click OK .
Click Options , and then in the Options or Solver Options dialog box, choose one or more of the following options:
In the Solver Parameters dialog box, click Solve or Close .
Click Load/Save , enter a cell range for the model area, and then click either Save or Load .
Tip: You can save the last selections in the Solver Parameters dialog box with a sheet by saving the workbook. Each sheet in a workbook may have its own Solver selections, and all of them are saved. You can also define more than one problem for a sheet by clicking Load/Save to save problems individually.
On the Select a Solving Method pop-up menu, select one of the following:
Note: Portions of the Solver program code are copyright 1990-2010 by Frontline Systems, Inc. Portions are copyright 1989 by Optimal Methods, Inc.
Because add-in programs aren’t supported in Excel for the web, you won’t be able to use the Solver add-in to run what-if analysis on your data to help you find optimal solutions.
If you have the Excel desktop application, you can use the Open in Excel button to open your workbook to use the Solver add-in .
More help on using Solver
For more detailed help on Solver contact:
Frontline Systems, Inc. P.O. Box 4288 Incline Village, NV 89450-4288 (775) 831-0300 Web site: http://www.solver.com E-mail: [email protected] Solver Help at www.solver.com .
Portions of the Solver program code are copyright 1990-2009 by Frontline Systems, Inc. Portions are copyright 1989 by Optimal Methods, Inc.
Need more help?
You can always ask an expert in the Excel Tech Community or get support in the Answers community .
Using Solver for capital budgeting
Using Solver to determine the optimal product mix
Introduction to what-if analysis
Overview of formulas in Excel
How to avoid broken formulas
Detect errors in formulas
Keyboard shortcuts in Excel
Excel functions (alphabetical)
Excel functions (by category)
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Miss Manners: Can society ever solve the work/life balance problem?
- Published: Mar. 06, 2023, 8:00 p.m.
- Judith Martin
GENTLE READERS: The clash between people who don’t want to return to the office (employees) and those who want them to do so (employers) is no surprise to Miss Manners. The pandemic might have brought this out, but the work/private life problem has existed throughout history.
Society needs to provide both. Obviously, it needs workers. But it also needs people to attend to family life, community welfare and functions of leisure, recreation and entertainment, as these promote general satisfaction.
Therefore, society has, in different eras, come up with different solutions to staff both realms. And all of them have been terrible.
For centuries, the division was the one that seemed most reasonable to those with the power to enforce it: The poor would work, with only enough of a private life necessary to produce another generation of workers. This freed the rich to pursue such leisure activities as socializing, sports and, when things got really dull, warfare.
But in the 19th century, the Industrial Revolution produced a class of people who were neither rich enough not to work, nor poor enough to put up with forgoing pleasure. So the division changed: All the poor would still work and the rich play, but among the reasonably solvent, males would earn money working, and females would perform the functions that did not pay.
This was adjusted in the mid-20th century to admit females to certain paid jobs (notably, those lacking in prestige), even if for less pay and fewer opportunities to advance. Ever since then, efforts have been made to give females the work advantages that males enjoyed -- including the same work schedule.
But just as the school schedule remains as designed under the presumption that children needed to be free in the summer to help with the crops, the work schedule remains as it was under the presumption that the worker had a partner taking care of the private realm.
The underlying problem was hardly addressed: Who would staff that private realm? For the essential parts, household and child care, it has been either the better-paid female worker or one in a poor-paying job. And the merely enjoyable parts, chiefly family and social life, suffered from neglect.
So that solution didn’t work, either -- and people are finally noticing.
Whatever compromise might be worked out eventually will take a great deal of negotiating. Employers, as well as employees, have legitimate concerns about work time and place that must be addressed.
Miss Manners’ contribution is to point out that the easiest part to cut is the pseudo-social life that has become a feature of business models: what is now referred to as “mandatory fun.” Surely workers no long believe that after-hours drinks, office birthday celebrations and team-building exercises are adequate substitutes for time spent with people of their own choosing.
And bosses will find that encouraging a cordial, cooperative, cheerful level of professional behavior will be easier and more productive than trying to make employees love one another.
DEAR MISS MANNERS: Can I touch up my lipstick at the dinner table?
GENTLE READER: You’ll only get it all over your fork and glass.
(Please send your questions to Miss Manners at her website, www.missmanners.com ; to her email, [email protected] ; or through postal mail to Miss Manners, Andrews McMeel Syndication, 1130 Walnut St., Kansas City, MO 64106.)
COPYRIGHT 2023 JUDITH MARTIN
DISTRIBUTED BY ANDREWS MCMEEL SYNDICATION
1130 Walnut St., Kansas City, MO 64106; 816-581-7500
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Joe Biden Has One Problem He Can Never Solve
But Fox is attempting at a deeper implication: that Joe Biden is too old for the presidency ; that Biden is struggling on account of his advanced age .
And he may be struggling on account of his advanced age.
As I said, it’s a non-story.
Biden is too old
My concerns are even divorced from Biden’s ability to be mobile. Franklin Delano Roosevelt was arguably the best president ever and he couldn’t walk. John F. Kennedy, Jr. was functionally crippled but still cognitively sharp. Ambulation in no way relates to someone’s ability to successfully perform the essential duties of the presidency.
Harrison Kass is a Senior Defense Editor at 19FortyFive. An attorney, pilot, guitarist, and minor pro hockey player, he joined the US Air Force as a Pilot Trainee but was medically discharged. Harrison has degrees from Lake Forest College, the University of Oregon School of Law, and New York University’s Graduate School of Arts & Sciences. He lives in Oregon and regularly listens to Dokken.
March 7, 2023 at 2:22 pm
FDR was socialism. FDR was and is a threat to the Republic.
March 7, 2023 at 5:35 pm
Biden stumbling while negotiating a stairwell is not much to worry about.
What is to be worried about is his mental capacity or acuity what with his multiple covid infections, intermittent bouts of cancer, bse and dementia and seeing presence of dead people or dead or bygone nurses.
Clearly, his brain is totally suspect and that has been shown by him hurling billions of bucks over to the war in europe while migrants crash tbe southern borders while domestic inflation gets energized on a daily basis.
Biden is finished even as his doctors attempt to probe his disease-addled body for more undetected cancerous lesions.
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Can you solve it? The science of streaming
How to count without counting
UPDATE: To read the solution click here
Today’s puzzle is tricky! I mean trickle-y. It is all about streams.
The source of the puzzle is a ‘streaming algorithm’, which is a type of procedure in computer science that analyses data as it arrives in a stream, rather than waiting for the data to be stored in a memory.
The first streaming algorithms were devised in the 1980s. The idea behind them was to get an overall readout of incoming data as fast as possible, using as little memory as possible. Since data streams are ubiquitous in the digital world – phone calls, credit card transactions and Netflix movies, for example, are all data streams – this kind of algorithm is too.
You are about to meet one of the most important early streaming algorithms. Well, you are if you solve today’s puzzle. Buffering now!
The big ballot brainteaser
An election is held between candidates A, B, C and D. You are given a set of 100 completed ballot papers and your job is to work out whether any of the candidates has an overall majority, i.e. won 51 or more votes. If a candidate has done so, you must say who it is.
But there’s a catch. You are not allowed to count the ballot papers. That is, you are not allowed to use numbers in any way. You can’t write anything down, nor are you allowed to keep track of the tally in your memory. Instead you will have to devise a clever strategy that involves making instant decisions about each ballot paper when you see it.
All you are allowed to do is to move the papers between three piles on a table. The starting position, as illustrated below, has all the papers in a stack on the first pile. The ballot papers are face up, so you can always see which candidate has received a vote on the ballot paper at the top of the pile. There are two other positions for piles, but as yet they are empty.
There are only two options to start. You move the top ballot on Pile 1 to either Pile 2 or Pile 3. For your next move you can do the same again, or you can move the ballot that is on either Pile 2 or Pile 3 to another pile. And so on. At any stage all you can do is to move the ballot paper that is at the top of one pile to the top of another pile.
Your task is to find a strategy that tells you if one candidate has an overall majority (i.e 51 or more votes) simply by shifting ballot papers between piles. Can you do it?
As is often the case, it is helpful to simplify the problem to see if it gives us any insights. Let’s consider the case when there are only 2 candidates, A and B.
A simple strategy is as follows: if we see A atop the first pile, we put it on the second pile, and if we see B atop the first pile, we put it on the third pile. After 100 moves, the first pile will be empty, the second pile will have all the As and the third pile all the Bs. We can now work out which pile has the most ballots by placing them alternately back on the first pile. If there are any ballots left on the second pile at the end, then A has at least 51 votes, and if there are any ballots left on the third pile, then B does. Call this the “two-group strategy”.
Now try scaling up to four candidates, A, B, C and D. One way to do it would be to use the two group strategy with the candidates divided into two coalitions, say A&B vs C&D. If one of the coalitions has more than 51 votes, we then do the two group strategy twice more – once for each member of the winning coalition. This strategy works, but it is not very efficient: it relies on moving papers between piles at least 500 times, as well as keeping tracks of coalitions. There is a much quicker way. Can you find it?
I’ll be back at 5pm UK with a solution and a discussion. PLEASE NO SPOILERS instead discuss your favourite streaming services.
UPDATE: Click here to read the solution.
If you are wondering what moving ballot papers has got to do with streaming, here’s the analogy. Each ballot paper is a piece of incoming data. You are not allowed to count, which is analogous to not being able to use a memory to store information. Instead, you must make an instant decision about what to do as soon as each piece of data arrives, with the hope that very quickly you can learn some overall property of the whole stream: whether or not there is a majority value, and if there is, what it is.
Today’s puzzle was devised by Pierre Chardaire, a retired computer scientist.
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me .
I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.
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Vice President Kamala Harris took a tour of the Armand J. Brinkhaus Community Library in Sunset. Following the tour, she discussed the administration's $277 million investment to expand broadband to communities across Louisiana and the country.
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Ron Faucheux: How do you solve a problem like Kamala?
- BY RON FAUCHEUX
- Mar 5, 2023 - 6:00 pm
Vice President Kamala Harris is a difficult problem for Joe Biden to solve. Her poll ratings are weak and her job performance has been a big disappointment to many Democrats. Stories about her lack of preparation and office mismanagement are already legend.
The vice president’s inability — or, perhaps, refusal — to tackle complex issues when she had the chance, such as border security and immigration reform, has been an embarrassment.
If Biden runs again, he’ll be 82 soon after the election. His age would make his vice-presidential pick that much more important. Even though he’s likely to keep Harris on the ticket, Democratic operatives are increasingly concerned how voters will react to her remaining a heartbeat away from the presidency for another four years.
There’s nothing new about vice presidents being political liabilities or getting dumped at reelection time. Replacing a running mate, nevertheless, is a delicate matter.
Aaron Burr, who ran for vice-president with Thomas Jefferson in 1800, secretly tried to get the Electoral College to elect him president instead. Four years later, Jefferson barred Burr from the ticket and later ordered his arrest as a traitor.
Abraham Lincoln rarely saw his vice president, Hannibal Hamlin, who oddly served as a guard and company cook during the last part of the Civil War. He was replaced on the ticket in 1864 by Andrew Johnson, who became president when Lincoln was assassinated less than six weeks into the new term.
Ulysses Grant’s first vice president was implicated in a scandal and defeated for re-nomination. Grover Cleveland ran three times for president, winning twice. In each race, he had a different running mate.
Franklin Roosevelt’s selection of House Speaker John Nance Garner as vice president was the result of a deal for delegates at the 1932 Democratic convention. Never close to FDR, Garner stayed on the ticket in 1936 but was shown the door in 1940 when Henry Wallace, the agriculture secretary, replaced him.
In 1944, a gravely ill FDR sought a fourth term. Democratic bosses feared that Wallace, a left-wing mystic, would succeed to the presidency if he remained vice president. The wily FDR secretly allowed party leaders to sideline Wallace, throwing open the vice-presidential nomination at the convention. The prize went to Sen. Harry Truman. After only 10 weeks as vice president, Truman became president when Roosevelt died.
The last vice president to be excluded from the ticket was Nelson Rockefeller in 1976. When Gerald Ford became president upon Richard Nixon’s resignation, he appointed the former New York governor to fill the second spot. But after a strong challenge from Ronald Reagan in GOP primaries, Ford needed to strengthen his right flank. He couldn’t do it with Rockefeller, a moderate. A hard-bitten realist, Rockefeller understood the game; he graciously offered to withdraw, and Ford accepted.
Getting dumped as vice president isn’t necessarily a career killer. Hamlin, thereafter, was appointed Collector of the Port of Boston and Minister to Spain, and even went back to the U.S. Senate for two more terms. A disgruntled Wallace was given the job of secretary of Commerce as consolation; he later ran as a third-party candidate for president.
Would Harris step aside, as Rockefeller did? Would she do it to keep Donald Trump or Ron DeSantis from winning? It’s unlikely for two reasons: First, her historic role as the nation’s first woman, African American and Asian American vice president would make it difficult to leave the ticket. Second, Harris still wants to be president.
If Biden doesn’t run again, Harris likely will. But if her next presidential campaign is anything like the last one, she’ll have an uphill climb. When Harris started her 2020 White House bid, pundits thought she had great potential. After spending $42 million, she dropped out before any votes were cast. Polls showed she lacked support from key constituencies, particularly women and Blacks.
Democrats rightly fear that Harris, if she becomes their presidential nominee in 2024, would lose to either Trump or DeSantis. That makes her a problem right now for both Biden and the party. But at some point, they need to figure out, as "The Sound of Music" song ponders, “How do you keep a wave upon the sand?”
Ron Faucheux is a nonpartisan political analyst, pollster and writer based in Louisiana. He publishes LunchtimePolitics.com , a nationwide newsletter on polls and public opinion.
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India says its infrastructure boost could create much-needed jobs. Economists aren't so sure
India is pumping up its infrastructure spending, a move the government says will create much-needed jobs.
- However, economists who spoke to CNBC aren't so optimistic about the number of jobs that can be created from a surge in infrastructure investments.
High unemployment remains a challenge for India, and has been one of the biggest criticisms against the government of Prime Minister Narendra Modi.
At the annual budget announcement in February, the finance ministry said it will be pumping up capital expenditure by 33% to 10 trillion rupees ($120.96 billion) , as India is set to be the world's fastest growing economy .
However, economists who spoke to CNBC aren't so optimistic. They say the number of jobs that can be created from a surge in infrastructure investments may be fewer than the government expects.
The government's focus is "completely wrong" and its policies are "completely against employment generation," said Arun Kumar, a retired economics professor from New Delhi's Jawaharlal Nehru University.
"Capex is not the answer, but how the capex is going to be used," Kumar said, highlighting that not enough money is being pumped into creating "labor intensive" jobs in India.
What's the problem?
Employment in India is divided into different sectors: organized and unorganized.
Businesses in the organized sector are often licensed by the government and pay taxes. Employees are usually full-time staff and have a consistent monthly salary. Companies in the unorganized sector are usually not registered with the government and employees work ad hoc hours with irregular salaries.
When people in India are "too poor not to work," they'll result in doing "residual work" with very low incomes such as driving rickshaws, carrying luggage, or even selling vegetables on the street, Kumar said.
According to Kumar, the organized sector only makes up 6% of India's workforce. On the other hand, 94% of jobs are in the unorganized sector — with half the jobs in agriculture.
As India's infrastructure sector becomes more reliant on technology and automation, the upcoming boom in projects will create jobs for the organized sector, Kumar said. A lack of investments in the unorganized sector hence leaves many stuck with unstable jobs without a fixed income.
Those employed in agriculture are also "stuck" with low salaries since inadequate investments leave little room for them to upskill, Kumar said.
According to the Centre for Monitoring Indian Economy, an independent think tank, unemployment rose to a 16-month high at 8.3% in December 2022, but dipped to 7.14% in January.
CNBC reached out to the Ministry of Finance and is waiting for a response.
A more technologically advanced infrastructure sector also means fewer jobs will be available for those in the organized sector, Chandrasekhar Sripada, professor of organizational behavior at the Indian School of Business said.
"New generation manufacturing is not labor intensive. The number of jobs it can create at the unit-level will not be as high as it used to be," Sripada said. "In the 1950s, if we set up a steel plant, we would employ 50,000 people. But today … we will employ 5,000 people."
Who's most affected?
Sentiment in India's job market remains weaker than some countries in the region as a result of a mismatch of skills.
India's labor force participation rate — or the number of active workers and people looking for jobs — came in at 46% in 2021, according to data from the World Bank. That's lower than some other developing nations in Asia, such as 57% for Bangladesh and China at 68% in the same year.
Female work participation rate also dropped from 26% in 2005 to 19% in 2021, data from the World Bank showed.
"We've seen a very unexplainable drop in the participation of women in the labor force during Covid," Sripada said. "The caregiving responsibilities on women just increased far more and many dropped out of the workforce, and probably that hangover is continuing."
Even youth with college degrees are struggling to find jobs.
Youth unemployment, or those in the workforce between 15 to 24 years old with no jobs, stood at 28.26% in 2021 — that's a 8.6% higher than 2011.
Many of the youth living in rural areas are "semi-educated" because they have degrees in their hands but are not skilled enough to gain employment, Sripada said. It's also a challenge for employers to create jobs that target these people, he added.
"We have enough colleges to provide bachelor degrees, but these degrees ... do not prepare them with enough skills to get employment," he said.
Scientists Finally Solve Mystery of Why Solar Probes Keep Fogging Up
Space probes designed to study the Sun are the last places you'd expect to have a moisture problem. Yet a recent investigation has found aluminum filters on two different satellites are degrading as water corrodes their surfaces.
The filters help detect extreme ultraviolet (EUV) emissions, so any kind of clouding is bound to affect their effectiveness. Though the issue has been evident for a while, scientists now finally know what's causing it.
NASA's Solar Dynamics Observatory ( SDO , launched in 2010), and NASA and the European Space Agency's Solar and Heliospheric Observatory ( SOHO , launched in 1995) both have the same issue. In the first six months, SOHO's Solar EUV Monitor degraded by about 35 percent; in the five years following, it degraded by a further 60 percent.
Solar probes aren't exactly cheap, and neither is launching annual recalibration missions to send new sensors into space. Figuring out why the filters are clouding could see to future solar probe missions being made more robust.
In 2021, a team of scientists led by physicist Charles Tarrio of the National Institute of Standards and Technology (NIST) experimentally figured out what it wasn't – that is, a build-up of carbon causing the fogging, long considered the culprit.
Now they've figured out what it is, and it's surprising: oxidation of the aluminum, caused by the presence of water and induced by ultraviolet radiation. As the layers of oxidized metal build up, the filter becomes foggy, preventing it from admitting the light waves the sensor is designed to monitor.
The surface of aluminum is usually naturally coated with a surface layer of oxide, which occurs when oxygen atoms bond to the atoms on the surface of the aluminum. UV light increases the oxidation rate, causing additional layers of oxide to form.
There's usually not a lot of oxygen in space to bond to the aluminum, but the presence of water, which contains oxygen atoms, could be a game-changer.
To test the water hypothesis, the researchers used the NIST's Synchrotron Ultraviolet Radiation Facility (SURF) to generate EUV radiation, blasting it at an aluminum filter in a vacuum chamber into which water vapor had been introduced.
In their experiments, Tarrio and his team did indeed find a layer of oxide on their aluminum sample that was much thicker than suggested by accepted theory, although not quite as thick as those seen on solar probes. Modeling, however, showed that with sufficient exposure – around 10 months – they would have achieved an oxide layer comparable to aluminum filters on space probes.
Their solution to the mystery, the researchers said, was a " one-two punch ."
"Punch one was physically showing that this chemical process involving water could cause something comparable to what we actually see happening in the satellites. And the number two punch is saying once you create a theoretical model that takes everything into account, then the numbers line up quantitatively with what we see in the satellites," explains physicist Robert Berg of NIST.
"Putting everything together, I'm convinced. Water is responsible for the filter degradation."
The next question is where on Earth did the water come from? The team believed that it had to have somehow hitch-hiked a ride on the probes themselves.
"It had to be something that can emit water for five years continuously at reasonably constant rates," Tarrio says . "That set Bobby [Berg] off on this quest to find, what the heck could this be? What could be a source that fits? And he found it."
The answer, to be detailed in an upcoming paper, is the thermal blanket material used to protect the delicate instruments of the probe from extreme temperatures. These are made of layers of a thin sheet of polyethylene terephthalate (PET), coated with reflective metal that reflects most of the heat that hits the material.
However, PET is known for absorbing and holding onto water from the atmosphere. So it goes into space with all this water retention and then, when the solar heat hits it, the water vaporizes and slowly outgasses, releasing into the spacecraft and causing the aluminum EUV filter to oxidize.
"It was hard," Berg says , "to think of anything else that would hold that kind of water."
Everything the Sun does is interesting, but solar flares and coronal mass ejections are of particular interest here on Earth. If they're unleashed in the direction of Earth, the quantities of matter flung towards us can trigger geomagnetic storms that risk interrupting satellite and radio communications, and even interfere with power grids.
This solar matter can take two to six days to reach us, so instruments that can detect their tell-tale waves of EUV radiation ahead of time are crucial for advance warning and predicting the strength of the geomagnetic storm to come.
In future work, the team hopes to explore ways to prevent this oxidization, whether by working on protecting the aluminum, or developing a new filter that can operate in the required wavelength range.
The research has been published in Solar Physics .
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The Sonos Era speakers solve a major problem for Android users
The new Sonos Era 100 and Era 300 usher in a new generation of wireless speakers for the company, and our first impressions were pretty good . They also close a gaping hole that has plagued a pretty large segment of users. Android users no longer are left out of the Trueplay feature.
Custom tuning of speakers for their environments isn’t particularly new. Google has done it with its Nest Hub Max. Apple does it with the HomePod. But Sonos has always required a phone to do the listening for ambient sound and fine-tuning the speakers. And to date, that phone always has had to be an iPhone (unless you have a portable Sonos Move , but that’s almost a different product category at this point. Stay with us here).
It’s as simple as that, and Sonos keeps its messaging about the change just as simple in its press release. “Using the microphone array in Era 100 and Era 300, Trueplay optimizes the sound for the unique acoustics of your space with just a tap in the Sonos app.”
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It’s worth at least acknowledging that while having Trueplay in the new generation of Sonos speakers fixes things going forward, it doesn’t change the status quo for Android users who already have a Sonos speaker. Even the old Sonos Play:1 allows for Trueplay — again, only if you have an iPhone — and the new hardware does nothing to change that fact.
But if you’ve got an Android phone and are in the market for a new Sonos speaker, you’ll at least no longer be left out of the Trueplay fold.
The new Sonos Era 100 and Era 300 are available for preorder now and will be available on March 28. The Era 100 runs $249, and the Era 300 costs $449.
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If you're the sort who prefers to watch your MLS games from the comfort of your favorite barstool instead of your couch, you're in luck. DirecTV today announced that it's reached an agreement with Apple and Major League Soccer to make MLS Season Pass available to more than 300,000 restaurants, bars, hotel lounges, and more for the 2023 MLS season, via existing satellite equipment.
While that doesn't necessarily mean that every match will be available on every TV, it means those games will be available. So you might still have to fight for screen time alongside the likes of college basketball, baseball, and football — but that's nothing a strategically placed $20 probably can't handle.
T-Mobile today announced that it's giving its subscribers MLS Season Pass for free. The service — which gets you every MLS game this season, along with other attached leagues — normally costs $100 for the season, or $15 a month.
T-Mobile subscribers (and Metro by T-Mobile customers) will be able to add MLS Season Pass via the T-Mobile Tuesdays app starting on February 21.
Bose is pushing out a software update that will grant users of its QuietComfort Earbuds II (QCE II) the ability to use either earbud independently. At launch, only the right earbud could be used on its own. To get the new software, you'll need to open the Bose Music app and connect the QCE II to your phone. If you don't see a notification to perform the update, check back later in the day as Bose says the updates will be going out on a rolling basis starting February 16.
Once the update is complete, you'll be able to use either just the left or right earbud for listening to content and taking or making calls. You'll also be able to seamlessly switch between your earbuds and if one earbud runs out of battery life or disconnects from Bluetooth, you can continue listening with the other earbud without interruption, according to Bose.
The U.S. Army Has a Recruitment Problem. Here's How to Solve It
T he difficulty of recruiting the U.S. Army’s next generation has become not only one of the biggest challenges for the future of the force, but also perhaps its biggest political football.
When Army leaders projected late last year that active Army troop strength for 2023 would have a shortfall of almost 20,000 from the projected 485,000, it quickly led to action inside the force and heated debate outside. Army Secretary Christine Wormuth and Chief of Staff General James McConville announced they would shift up to $1.2 billion from Army programs to recruiting initiatives, enlistment and reenlistment bonuses, and other efforts. In turn, worries about what the personnel shortfall meant and its connection to some of the most hot-button political issues became a talking point everywhere from cable news shows to congressional hearings .
Yet, the reality of the issue is not what much of the controversy has made it seem. The actual causes of the recruiting problems, and thus measures we should take in answer to them, don’t match where so much of the attention is being paid.
Despite receiving so much attention in the media and our politics, Army leaders note that there is literally no “hard data” indicating that the cause of the shortfall is a COVID-19 vaccine mandate (which has been rescinded anyway ). The numbers of its effect on retention don’t add up either. According to Defense Department records , 1,816 soldiers have been discharged for refusing to receive vaccinations, which is a relatively small proportion of the service and the gap. U.S. defense officials believe that the resistance of the vaccination results from misinformation about the safety of the vaccination
Similarly, the data doesn’t support the idea that “woke-ism” and a focus on social justice is behind the recruiting gap. As the commanding general of the U.S. Army Recruiting Command, Major General Johnny Davis, told Defense One, “While there are many things that prevent young Americans from enlisting in the military, including a lack of awareness about military life in general, ‘woke-ism’ is not one of them.” This finding has been backed by the latest Army surveys , which queried some 2,400 youth between the ages of 18 to 25 on their attitudes toward the service.
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Experts who study the issue agree. As Lindsay Cohn, an associate professor of national security affairs at the Naval War College, told a recent conference on the topic, there is plenty of data showing why young people don’t join the military, but “wokeness is not on the list. ” Indeed, by the raw numbers, there have been over four times more articles, op-eds, cable news interviews, think-tank reports, and angry web posts on the issue of wokeness deterring service (87,000 at last count) than the actual number of recruits in the gap.
It is also valuable to understand the historic and current context around the Army’s recruiting gap. For instance, shortfalls are not new to the force. As it enters the 50th year of the all-volunteer force, the Army has experienced multiple periods of recruiting highs and lows, from the surges in the wake of 9/11 patriotism to similar difficulties in recruiting following the Vietnam War and during the Iraq War. It has also regularly been lifted or buffeted by the surrounding economy, with today’s low unemployment rate being good for job prospects, but tougher for military recruiting.
Nor is the current recruiting challenge unique to the U.S. Canada’s armed forces presently have such a far more severe shortage, such that about 1 in 10 of its military’s 100,000 positions are unfilled. In turn, even the U.S.’s new strategic competitors face recruiting challenges. Russia’s army has had to turn to conscription and the use of prisoners to fill out its ranks during the Ukraine war, while the People’s Liberation Army is scrambling to fill gaps in well-educated young troops, leading China’s top leader, Xi Jinping, to call for a greater “sense of urgency” on military-personnel modernization at both the 19th and 20th Party Congresses.
Finally, it is notable that, despite the fact that they all operate under the very same supposed problems of vaccine mandates and wokeism, the recruiting issues differ across the U.S. military services. In fact, General John “Jay” Raymond, the new Space Force’s first chief of staff, recently told an event that his service has the opposite problem as the Army. “We have more people knocking on our door than we can take,” Raymond said.
So what is actually happening, and what can be done to have a real effect? The short answer is that the Army faces a combination of challenges beyond its control that link to problems of its own making. Fortunately, each has a ready set of responses in three areas.
First is to widen a shrinking pool. Put directly, less young Americans are eligible to serve than in the past, due to changing demographics, education performance, and especially health (weight, behavioral health, and other medical conditions). Only 23% of American youth fully meet the Army’s eligibility requirements, compared to 29% in the previous years.
Obviously, long-term efforts to aid such social problems would be helpful, yet the Pentagon has multiple ways to face this better in the here and now. The first is that the requirements are not uniform across the U.S. military; the Army and its peers are drawing from the same pool, but with different standards. According to our discussions with Lieut. Colonel Felichia Brooks, a Battalion Commander with the Baltimore Recruiting Command, the organization has lost multiple applicants to other services because of these differences. Fixing these enlistment eligibility disparities should be on the action list.
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The second is to recognize that no matter how standards are applied, the problem of societal demographic and health aren’t going away. As such, more is required to aid would-be recruits to meet these standards. For example, a pilot program called the Future Soldier Preparatory Course has met with great success at Fort Jackson in South Carolina to help overcome obstacles to military duty related to academic performance and physical health barriers. Such programs could be scaled more widely.
It would also be valuable to widen the pool by updating outdated policies that are presently excluding potential recruits. Here there are also two ready responses. Regulation (AR) 600-85 of the Army Marijuana and the Army’s Substance Abuse Program penalizes would-be recruits for using a substance now accepted in more than 20 states and the District of Columbia. It could be modified to reflect that if marijuana use is permissible in the state where the applicant enlists, then the Army must consider the laws of that state. It is upon enlistment, not before, that recruits should be limited to Army’s Drug and Alcohol policies.
Finally, the Army must change to reflect the new American family. There are over 11 million single parent households in the U.S. now, of whom a quarter face joblessness or economic challenges. And yet, under current Army policy, single parents must give up guardianship of their children for their initial enlistment. The resulting duration could be anywhere between two years to a lengthy six years, which creates an obvious barrier to entry for single parents. Yet, the Army has successfully navigated having single parents inside the force for decades. At last count, in 2021 , there were 119,186 single parents successfully serving in the U.S. military, nearly half of them in the Army. The force should therefore explore adjusting its current policy to allow recruits to regain custody of their children within an earlier stage of their service, such as 12 to 18 months on active duty.
The second area of shift needed is to reform the Army’s own systems and bureaucracy, to reduce anything hampering the recruiting process. Too many barriers are thrown up for those showing interest in the force, something all the worse among a generation that experiences quick responses in so many other parts of their lives. For instance, the Army recently put into place a program called GENESIS, an automated and integrated medical information system that aids in managing and providing health care. Although it has the laudable goal of performing a more thorough medical screening of applicants and boosting medical screening efficiency, it has caused significant processing delays for applicants. These can extend sometimes as long as a year, according to Brooks, resulting in many applicants choosing an alternative military service than the Army or even a civilian job that offers a much quicker on-ramp.
A recruit for the Army shouldn’t be lost because of protracted red tape and a burdensome documentation process. To decrease medical delays, the Army must consider authorizing the United States Military Entrance Processing Command permission to hire more medical personnel to review and handle medical waivers to reduce delays.
The final track is to build up the awareness and attraction of the Army. As Major General Alex Fink, chief of the Army’s Enterprise Marketing team, noted after the survey results came out, the issue for today’s youth wasn’t vaccines or wokeness, but they “just don’t see the Army as something that’s relevant.”
In this public outreach effort, though, Army recruitment has been behind the eightball in its branding. When it first shifted from a draft to a professional force, the Army messaged “Be All You Can Be.” It was considered one of the best slogans in not just the history of military recruiting, but all of advertising.
In 2001, though, the Army jettisoned the tried and true and spent the next two decades cycling through new mottos and campaigns, from “Army Strong” and “Army of One” to the present “What’s Your Warrior?” The current campaign was actually adapted in 2018 in a deliberate attempt by Army leaders to find a new slogan they hoped would be “as powerful as Be All You Can Be.”
Unfortunately, the video-game-derived question has failed to resonate both with youth it targeted and the equally important set of parents, coaches, and teachers who advise them.
As a result, this year, the Army will debut a new marketing initiative. It turns out the best course of action was to return to the slogan “Be All You Can Be.” The force is going back to the slogan because it better “conveys the possibilities that await a new Army recruit,” as Fink explains.
A better message, though, will only go so far. Less than 1% of the population is a military member; hence, most Americans do not have personal connections to understand Army life and its opportunities (which the survey data shows is more of a barrier). Thus, the Army must step up its community outreach activities at every command. As Wormuth and McConville put it, “We are in a war for talent, and it will take all of our people — troops from all components, families, Army civilians, and soldiers for life — to fight and win this war.”
This recruiting “war” will only be won if actual organizational incentives and leader evaluations are changed to reflect the force’s needs. We must turn outreach into a real whole-of-force effort, with the inducements to match. An example start is a pilot program that mirrors how civilian industry recruits; successful companies don’t just rely on their HR department in a job search, but also enlist their own employees’ peer networks. The new Army pilot similarly rewards enlisted soldiers who personally aid recruiting, by providing them with a promotion if their referral draws another soldier into the force.
For all the controversy that surrounds the Army’s recruiting shortfall, its answers lie in reflecting the world we live in. The successful force of tomorrow will be built not from the angry debate but from sound policy. And that may be the best outcome of all.
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