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## 17 Hard Math Problems That’ll Make Your Head Spin

## These brain-teasing hard math problems are tricky, but they'll give your brain a workout—and they're really rewarding when you figure one out!

## Time to test your brain!

## Track and field

## Answer: Space 19

## Ones and zeros

## Answer: 1100

Which number should be on the bottom left stamp? (Hint: It’s a one-digit number.)

## Energy saver

## Symbol sums

## Answer: – , + , ÷

## Rack ’em

## Number music

Most of these are just simple math, or even common knowledge (a fourth of 100)!

## Do the math

Here’s another one that probably just takes some time and several incorrect guesses.

Which pins do you have to knock over to get a total of 100 points?

## Answer: 13, 39, and 48

What time is the last appointment?

## Answer: 19.50

Which blocks should go in Space A and Space B?

## Answer: Block 2 in Space A and Block 0 in Space B

## Number blocks

What number should replace the question mark on the bottom right loop?

## Answer: Letter d

## It’s a sign

What number should go on the bottom right sign?

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## 20 Grade-School Math Questions So Hard You'll Wonder How You Graduated

## 1. Question: What is the number of the parking space covered by the car?

## Answer: 87.

## 2. Question: Replace the question mark in the above problem with the appropriate number.

This problem shouldn't be too difficult to solve if you play a lot of sudoku.

## 3. Question: Find the equivalent number.

This problem comes straight from a standardized test given in New York in 2014.

## 4. Question: How many small dogs are signed up to compete in the dog show?

## Answer: 42.5 dogs.

## 5. Question: Find the area of the red triangle.

## 6. Question: How tall is the table?

## Answer: 150 cm.

## 7. Question: If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

This problem, mathematically speaking, is very similar to one of the other ones on this list.

## Answer: $0.05.

## 8. Question: When is Cheryl's birthday?

If you're having trouble reading that, see here:

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?"

## Answer: July 16.

## 9. Question: Find the missing letter.

This one comes from a first grader's homework.

## Answer: The missing letter is J.

## 10. Question: Solve the equation.

This problem might look easy, but a surprising number of adults are unable to solve it correctly.

## 11. Question: Where should a line be drawn to make the below equation accurate?

## Answer: A line should be drawn on a "+" sign.

## 12. Question: Solve the unfinished equation.

Try to figure out what all of the equations have in common.

## Answer: 4 = 256.

The formula used in each equation is 4 x = Y. So, 4 1 = 4, 4 2 = 16, 4 3 = 64, and 4 4 = 256.

## 13. Question: How many triangles are in the image above?

## Answer: 18.

## 14. Question: Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks.

## Answer: 13.3922.

## 15. Question: There is a patch of lily pads on a lake. Every day, the patch doubles in size…

## Answer: 47 days.

## 16. Question: How many feet are in a mile?

## Answer: 5,280.

This was one of the questions featured on the popular show Are You Smarter Than a 5th Grader?

## 17. Question: What value of "x" makes the equation below true?

## Answer: -3.

## 18. Question: What is 1.92 divided by 3?

You might need to ask your kids for help on this one.

## Answer: 0.64.

## 19. Question: Solve the math equation above.

## 20. Question: How many zombies are there?

Finding the answer to this final question will require using fractions.

## Answer: 34.

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## 40 Bad Heart Habits After 40

## Watch Out for This Heart Attack Warning Sign

## Eating More of This Cuts Heart Disease Risk in Half

## USPS Suspending Operations in These Places

These changes have already gone into effect.

## Walmart and Kroger Are Closing Locations

The first stores close on March 9.

## Lowe's Slammed for Military Discount Change

## Family Dollar Is Making Shopping Easier

Expect to see more products in stores.

## Bruce Willis' Wife Asks Paparazzi for "Space"

The star has been diagnosed with dementia.

## Pamela Anderson Used to "Hate" Her Appearance

Modeling for Playboy changed everything.

## These Are the 10 Hardest Math Problems That Remain Unsolved

The smartest people in the world can’t crack them. Maybe you’ll have better luck.

- How Many of These Tough Logic Puzzles Can You Solve?
- A Self-Taught Math Genius Wrote This Riddle While Serving Time in Prison. Can You Solve It?
- These Are the 10 Toughest Math Problems Ever Solved

## The Collatz Conjecture

## Goldbach’s Conjecture

## The Twin Prime Conjecture

## The Riemann Hypothesis

There is a function, called the Riemann zeta function, written in the image above.

## The Birch and Swinnerton-Dyer Conjecture

## The Kissing Number Problem

## The Unknotting Problem

## The Large Cardinal Project

## What’s the Deal with 𝜋+e?

## Is 𝛾 Rational?

## .css-8psjmo:before{content:'//';display:inline;padding-right:0.3125rem;} Math .css-v6ym3h:before{content:'//';display:inline;padding-left:0.3125rem;}

How the ‘Fourier Transform’ Gave Us Color TV

Solution to Riddle of the Week: Long Belt Problem

Can You Solve the Puzzle of Four Knights?

Solution to the Four Knights Puzzle

Can You Find the Most Absurd But Logical Answer?

Solution to the Interpretation Problem

We Already Know How to Build a Time Machine

Can You Calculate the Captain's Age?

Solution to the Captain’s Age Riddle

Can You Solve the Crate-Packing Riddle?

Solution to the Crate-Packing Riddle

## Choose Your Test

Sat / act prep online guides and tips, the 15 hardest sat math questions ever.

Image: Sonia Sevilla /Wikimedia

## Brief Overview of SAT Math

## But First: Should You Be Focusing on the Hardest Math Questions Right Now?

Now let's get to our list of questions (whoo)!

## The 15 Hardest SAT Math Questions

## No Calculator SAT Math Questions

- A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of $5/9$ degree Celsius.
- A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
- A temperature increase of $5/9$ degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.

A) I only B) II only C) III only D) I and II only

ANSWER EXPLANATION: Think of the equation as an equation for a line

Since ${9}/{5}$ = 1.8, statement II is true.

$$C= {25} /{81} (\which \is ≠ 1)$$

$$24x^2 + 25x - 47 = (-8x-3)(ax-2) - 53$$

You should then multiply $(-8x-3)$ and $(ax-2)$ using FOIL.

$$24x^2 + 25x - 47 = -8ax^2 - 3ax +16x + 6 - 53$$

Then, reduce on the right side of the equation

$$24x^2 + 25x - 47 = -8ax^2 - 3ax +16x - 47$$

If $3x-y = 12$, what is the value of ${8^x}/{2^y}$?

A) $2^{12}$ B) $4^4$ C) $8^2$ D) The value cannot be determined from the information given.

ANSWER EXPLANATION: One approach is to express

The fraction $1/6$ can also be rewritten as $0.166$ or $0.167$.

The final answer is $1/6$, $0.166$, or $0.167$.

$$({8-i}/{3-2i})({3+2i}/{3+2i})={24+16i-3+(-i)(2i)}/{(3^2)-(2i)^2}$$

Since $i^2=-1$, this last fraction can be reduced simplified to

$$ {24+16i-3i+2}/{9-(-4)}={26+13i}/{13}$$

$$AB =√{20^2-16^2}=√{400-256}=√{144}=12$$

$$sinF ={\opposite \side}/{\hypotenuse}={AB}/{AC}={12}/{20}={3}/{5}$$

The final answer is ${3}/{5}$ or 0.6.

## Calculator-Allowed SAT Math Questions

A) 0.410 B) 0.357 C) 0.333 D) 0.250

## Questions 8 & 9

Use the following information for both question 7 and question 8.

percent less than the average number of shoppers in the original store at any time.

## Question 10

$\bi b$ = $\bo 5 \bi r-\bo 4\bi p$.

Next, we can set the two equations equal to $b$ equal to each other and simplify:

Finally, to find $r/p$, we need to divide both sides of the equation by $p$ and by $4$:

The correct answer is B , $3/4$.

## Question 11

A) 261.8 B) 785.4 C) 916.3 D) 1047.2

$$V_{silo}=π(5^2)(10)+(2)({1}/{3})π(5^2)(5)=({4}/{3})(250)π$$

which is approximately equal to 1,047.2 cubic feet.

## Question 12

A) $m+6$ B) $m+7$ C) $2m+14$ D) $3m + 21$

$$[{m+9}/{2}+{2m+15}/{2}+{3m+18}/{2}]/3$$

This fraction can be simplified to $m + 7$.

## Question 13

ANSWER EXPLANATION: The equation $f(x) = k$ gives the solutions to the system of equations

$$y = f(x) = x^3-x^2-x-{11}/{4}$$

## Question 14

$$q_2 = (2.25)({1}/{2})n(v_1)^2 = (2.25)q_1$$

Therefore, the ratio of the dynamic pressure of the faster fluid is

$${q2}/{q1} = {2.25 q_1}/{q_1}= 2.25$$

The final answer is 2.25 or 9/4.

## Question 15

$${p(x)}/{x+k}=q(x)+{r}/{x+k}$$

Therefore, $p(x)$ can be rewritten as $p(x) = (x + k)q(x) + r$, where $r$ is a real number.

The question states that $p(3) = -2$, so it must be true that

$$-2 = p(3) = (3 + k)q(3) + r$$

A. $-2 = p(3) = (3 + (-5))q(3) + 0$ $-2=(3-5)q(3)$ $-2=(-2)q(3)$

This could be true, but only if $q(3)=1$

B. $-2 = p(3) = (3 + (-2))q(3) + 0$ $-2 = (3-2)q(3)$ $-2 = (-1)q(3)$

This could be true, but only if $q(3)=2$

C. $-2 = p(3) = (3 + 2)q(3) + 0$ $-2 = (5)q(3)$

This could be true, but only if $q(3)={-2}/{5}$

D. $-2 = p(3) = (3 + (-3))q(3) + (-2)$ $-2 = (3 - 3)q(3) + (-2)$ $-2 = (0)q(3) + (-2)$

This will always be true no matter what $q(3)$ is.

You deserve all the naps after running through those questions.

## What Do the Hardest SAT Math Questions Have in Common?

## #1: Test Several Mathematical Concepts at Once

Here, we must deal with imaginary numbers and fractions all at once.

## #2: Involve a Lot of Steps

Remember: the more steps you need to take, the easier to mess up somewhere along the line!

## #3: Test Concepts That You Have Limited Familiarity With

If you don't know your way around functions , this would be a tricky problem.

## #4: Are Worded in Unusual or Convoluted Ways

## #5: Use Many Different Variables

With so many different variables in play, it is quite easy to get confused.

## The Take-Aways

## What's Next?

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The 5 Strategies You Must Be Using to Improve 160+ SAT Points

How to Get a Perfect 1600, by a Perfect Scorer

## Series: How to Get 800 on Each SAT Section:

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How to Get a Perfect 36 ACT, by a Perfect Scorer

## Series: How to Get 36 on Each ACT Section:

## Series: How to Get to 24 on Each ACT Section:

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When should you take the SAT or ACT?

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Holly R. "I am absolutely overjoyed and cannot thank you enough for helping me!”

## The hardest viral math problems of the year

- People had mixed success trying to solve viral math problems this year.
- Some parents had trouble answering their kids' homework questions.
- A British mathematician presented a solution to a 160-year-old math problem that could make him a millionaire.

The internet seems to have a love-hate relationship with math.

Here are 11 math problems , brainteasers , and SAT questions that went viral this year.

## Only 2% of people were able to figure out this riddle in less than 60 seconds.

He wrote down the numbers one through 19 out of numerical order:

8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, ?, ?, ?, ?, ?

The completed set of numbers looks like this:

8, 18, 11, 15, 5, 4, 14, 9, 19, 1, 7, 17, 6, 16, 10, 13, 3, 12, 2

## This Chinese math question for fifth graders stumped adults.

How is the amount of cargo a ship contains supposed to help you figure out how old the captain is?

## This second grade math problem left the internet seriously confused.

## People couldn't agree on the answer to a question about buying and selling horses.

The man makes $10 with each sale, therefore he earns a total of $20.

## Author Ed Southall shared a math problem on Twitter that some people managed to get right.

Southall confirmed that the answer is indeed 1/3 .

## A math problem meant for 8-year-olds went viral after parents couldn't solve it.

Mumsnet user lucysmam turned to the internet for help with her daughter's math assignment.

"On the coast there are three lighthouses.

The first light shines for 3 seconds, then is off for 3 seconds.

The second light shines for 4 seconds, then is off for 4 seconds.

The third light shines for 5 seconds, then is off for 5 seconds.

All three lights have just come on together.

1) When is the first time all three lights will be off at the same time?

2) When is the next time all three lights will come on together at the same moment?"

For a more detailed explanation, click here .

## A tricky math problem created by Gergely Dudás used ice cream cones instead of variables.

## A Quora thread of difficult SAT math questions included one people called the "meanest test problem ever."

"In a class of p students, the average (arithmetic mean) of the test scores is 70.

In another class of n students, the average of the scores for the same test is 92.

When the scores of the two classes are combined, the average of the test scores is 86.

Talwalkar shared a step-by-step solution to the tough problem in a YouTube video.

There are a few ways to solve it, but Talwalkar presented a simple shortcut.

Turning that into an equation, we can easily figure out what p / n is:

## A British mathematician says he solved the "single most important open problem" in math after 160 years, but it still needs to be peer reviewed.

## This brainteaser has a missing number.

Read the first two rows of numbers horizontally, each as one number — 289 and 324.

## This brainteaser features three pentagons, each with a set of five numbers.

Visit INSIDER's homepage for more.

- Read more about math and science questions:
- 10 simple science questions that Americans struggle to answer correctly
- 15 common math questions from the SATs that everyone gets wrong
- 30 questions from the US citizenship test that even Americans might get wrong
- What standardized tests look like in 10 places around the world

Blog / Math / Hardest Math Questions That Are Surprisingly Easy To Solve!

## Hardest Math Questions That Are Surprisingly Easy To Solve!

## Check out These 10 Hardest Math Questions That will Test Your Logic and Problem-solving Skills

- Jamie Spafford on Twitter: “Here’s a riddle for you: If a baseball bat and a baseball together cost $1.10 and the bat costs a dollar more than the ball, how much does the ball cost? (H/T @ScottMonty for including it in his really great article: https://t.co/foD6RdOUgy)” / Twitter . (n.d.). Retrieved April 22, 2022, from https://twitter.com/jamiespafford/status/1290641293891317770
- 20 Tricky But Fun Grade-School Math Questions – Hard Math Problems . (n.d.). Retrieved April 22, 2022, from https://bestlifeonline.com/tricky-math-questions/
- 34 Hard Math Riddles and Word Problems for Future Geniuses | Fatherly . (n.d.). Retrieved April 22, 2022, from https://www.fatherly.com/play/hard-math-riddles-for-kids-with-answers/
- Southern Math Riddles Jeopardy . (n.d.). Retrieved April 22, 2022, from https://jeopardylabs.com/print/math-riddles-jeopardy

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## How to Work Through Hard Math Problems

## The Case for Doing Hard Things

## Strategies for Difficult Math Problems — and Beyond

Here are a few strategies for dealing with hard problems, and the frustration that comes with them:

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