Have you ever struggled enough with a math problem only to realize that it was too easy to solve? Many students will definitely vouch for it—a math question looked quite simple when they sat with it, but within minutes they understood that they had no idea how to solve it!

Sometimes you come across some of the most difficult math questions that are both challenging and brain teasers. Even if you are well-prepared for your exam, you will encounter difficult math questions. But here’s the thing: They can be solved in a flash, regardless of how ridiculously difficult they appear.

Yes, you heard that right! If you understand basic math skills and concepts, all you need are some math tricks and practice to solve the problems in a jiffy.

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

Interestingly, these hard math problems can be solved easily with basic math operators. Ready to test your math skills?

  • A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?

Answer: The ball costs 5 cents.
How did that happen? If you were thinking of some other answers to this problem, then this explanation might help you. Well, to simplify the question, the difference between $1 and 10 cents is 90 cents, not $1. The only way for the bat to cost a dollar more than the ball while still having the total cost equal to $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.

  • The classic PEMDAS problem: 6 ÷ 2(1+2) = ?

Answer: 9
Every PEMDAS problem leads to a huge disruption of opinions, splitting the masses into various answers while everyone believes that they have the correct answer. So, how was this solved and how did they arrive at “9” as the solution? If you remember the order of operations of PEMDAS from grade school, one generally works through the problem by solving parentheses, then the exponents, multiplication, and division, followed by addition and subtraction. Sometimes, some people interpret PEMDAS differently, and that is when the disagreement begins. According to the PEMDAS rule, one should solve anything inside parentheses, then exponents, and then all multiplication and division, starting from the left to the right, as per the operations.

  • Replace the question mark in the above diagram with an appropriate number.

Answer: 6
If you enjoy playing Sudoku, then this hard math problem would have been quite a breeze for you! The rows and columns all add up to 15, and that is how the answer turned out to be 6.

  • Solve the unfinished equation:

1 = 4

2 = 16

3 = 64

4 = ?

Answer: 4 = 256
Have a close look at the equation again, and find out the common thing among the equations. There is a formula that has been used for these equations. 4^x = Y. So, 4^1 = 4, 4^2 = 16, 4^3 = 64, and 4^4 = 256.

  • The Lily Pad problem: A lake has a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long will it take for the patch to cover half of the lake?

Answer: It will take 47 days for the patch to cover half of the lake.
If you assumed that half of the lake would be covered in half of the time, then your assumption could be incorrect. Here, in the math problem, it says that the patch “doubles” in size, which means, given any day, the lily pad was half the size the day before. So if the patch covers up the entire lake on the 48th day, it means the lily pad was half the size of the lake on day 47.

  • When you add five to nine, you get two. The answer is correct, but how?

Answer: Well, here’s the trick. When it is 9 a.m., you add five hours to it. Voila, you get 2 p.m. as your answer! Getting smarter every minute, aren’t we?

  • A group of students was standing in the sun facing due west on a march past event. The captain shouted at them: Right turn! About turn! Left turn! At the end of these commands, which direction are the students facing now?

Answer: East.
Well, this one might seem tricky, but the answer is quite simple. The students will first turn 90 degrees in a right turn and then 180 degrees in an about-turn. The students will finally turn 90 degrees in a left turn. Therefore, the students are now facing east.

  • Guess how many triangles are there in the above picture?

Answer: 18
This is another tricky math question where different people have come up with different answers. While some forget to count the hidden triangles, others forget to count the giant triangle. Why don’t you concentrate on the triangle again and find all the triangles?

  • How to make the following equation precise using three of these four mathematical symbols: + – × ÷ without following any order as such?

Equation: 21 _ 3 _ 18 _ 6 = 6

Answer: 21 – 3 + 18 ÷ 6 = 6
This is more of a symbol math problem than a PEMDAS problem. You can keep testing with the math operators until you find the correct answer.

  • John was asked to paint numbers outside 100 apartments. This means he will have to paint numbers one through 100. How many times will he have to paint the number eight?

Answer: 20 times
If you carefully read the question, the answer is within the question itself. It’s a tricky one, but this is how it goes: John paints on apartment 8, then he paints on apartment 18 (where the 8 digit comes up again) and, similarly, 28th, 38th, 48th, 58th, 68th, 78th, 80th, 81st, 82nd, 83rd, 84th, 85th, 86th, 87th, 88th, 89th, and 98th apartments.

These were some of the hardest math questions, which probably left your mind boggled. You can always keep improving your logical and math skills with these kinds of math problems that might seem difficult but are easier than you had thought. So, keep testing yourself with more tricky math problems and get your logical juices flowing.

To read more about versatile and new online techniques to improve your math concepts and boost your confidence in solving difficult problems, visit Byju’s FutureSchool blog.


  1. 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 
  1. 20 Tricky But Fun Grade-School Math Questions – Hard Math Problems. (n.d.). Retrieved April 22, 2022, from https://bestlifeonline.com/tricky-math-questions/ 
  2. 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/ 
  3. Southern Math Riddles Jeopardy. (n.d.). Retrieved April 22, 2022, from https://jeopardylabs.com/print/math-riddles-jeopardy 

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