There’s no better way to encourage outside-the-box thinking than math brain teasers. They’re usually much more about using logic than being a math whiz, so everyone will need to think creatively. Here are some of our favorite math brain teasers for students of all ages. They’re perfect for bell ringers, extra credit, or to fill the last few minutes at the end of class.
Math Brain Teasers
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1. Using only addition, add eight 8s to get the number 1,000.
Answer: 888 + 88 + 8 + 8 + 8 = 1,000.
2. Two years ago, I was three times as old as my brother was. In three years, I will be twice as old as my brother. How old is each of us now?
Answer: The older brother is 17, and the younger brother is 7.
3. If a hen and a half lays an egg and a half in a day and a half, how many eggs will half a dozen hens lay in half a dozen days?
Answer: 2 dozen, or 24 eggs.
4. When does 9 + 5 = 2?
Answer: When you’re telling time. 9:00 + 5 hours = 2:00.
5. A farmer had 17 sheep. All but 9 of them ran away. How many sheep does she have left?
Answer: 9.
6. A boy is 2 years old. His brother is half as old as him. When the first boy is 100, how old will his brother be?
Answer: 99.
7. Use the numbers 2, 3, 4, and 5 and the symbols + and = to make a true math equation.
Answer: 2 + 5 = 3 + 4.
8. If 3 cats can catch 3 bunnies in 3 minutes, how long will it take 100 cats to catch 100 bunnies?
Answer: 3 minutes.
9. Mr. Lee has 4 daughters. Each of his daughters has 1 brother. How many children does Mr. Lee have?
Answer: 5 (All of the daughters have the same brother.)
10. What single digit appears most frequently between and including the numbers 1 and 1,000?
Answer: 1.
11. Which weighs more: 16 ounces of feathers or a pound of solid gold?
Answer: They weigh the same. 16 ounces = 1 pound, no matter what material is being weighed.
12. Jake bought a pair of shoes and a shirt, which cost a total of $150. The shoes cost $100 more than the shirt. How much was each item?
Answer: The shoes cost $125, the shirt $25.
13. You have two coins that total 30 cents. One of them is not a nickel. What are the two coins?
Answer: A quarter and a nickel. (Only ONE of the coins is not a nickel!)
14. A + B + C = D, and A x B x C = D. What numbers make these two equations true?
Answer: A = 1, B = 2, C = 3, and D = 6.
15. Solve this in your head (no writing it down!). Take 1,000 and add 40 to it. Add another 1,000. Now add 30. Add another 1,000. Now add 20. Add another 1,000. Now add 10. What is the total?
Answer: 4,100.
16. Grandmother died and left half her money to her granddaughter and half of that amount to her grandson. She left a sixth to her brother, and the remainder, $1,000, to the animal shelter. How much did she leave altogether?
Answer: $12,000.
17. Your sock drawer contains 18 white socks and 18 blue socks. Without looking, what is the smallest number of socks you should take out to guarantee a matching pair?
Answer: 3.
18. You planted sunflower seeds in your garden. Every day, the number of flowers doubles. If it takes 52 days for the flowers to fill the garden, how many days would it take for them to fill half the garden?
Answer: 51.
19. There are 100 houses in the neighborhood where Alex and Dev live. Alex’s house number is the reverse of Dev’s house number. The difference between their house numbers ends with 2. What are their house numbers?
Answer: 19 and 91.
20. What can you place between 8 and 9 to make the outcome greater than 8 but less than 9?
Answer: A decimal (8.9 is greater than 8 but less than 9).
21. Multiply this number with any other number and you will get the same answer every time. What is the number?
Answer: Zero.
22. If there are 6 oranges in a basket and you take out 4, how many oranges do you have?
Answer: 4 (You took 4 oranges, so you have 4 oranges!)
23. There are 8 apples in a basket. Eight people each take 1 apple, but there is still 1 apple in the basket. How can this be?
Answer: The 8th person took the basket with 1 apple still in it.
24. Multiply all the numbers on the number pad of a phone. What is the total?
Answer: Zero (Phone number pads include the numbers 0-9.)
25. There are 7 kids in the Garcia family, each born 2 years apart. If the eldest Garcia child is 19, how old is the youngest Garcia child?
Answer: 7.
26. Two mothers and 2 daughters each had 1 egg for breakfast, but they only ate 3 eggs all together. How can this be?
Answer: There were only 3 people—a grandmother, her daughter, and her granddaughter.
Answer: 2 minutes. (It takes the front of the train 1 minute, and the rest of the train will take 1 more minute to clear the tunnel.)
28. I am a three-digit number. My second digit is four times greater than the third digit. My first digit is three less than my second digit. What number am I?
Answer: 141.
29. Tom was asked to paint numbers outside 100 apartments, which means he will have to paint numbers 1 through 100. How many times will he have to paint the number 8?
Answer: 20 times (8, 18, 28, 38, 48, 58, 68, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88 [two 8s], 89, 98).
30. Ellie works at the aquarium. When she tries to put each turtle in its own tank, she has one turtle too many. But if she puts two turtles per tank, she has one tank too many. How many turtles and how many tanks does Ellie have?
Answer: Ellie has 3 tanks and 4 turtles.
31. If eggs cost 12 cents a dozen, how many eggs can you get for $1?
Answer: 100 eggs (The eggs cost 1 penny each.)
32. If you toss a coin 100 times and it lands heads up every time, what is the chance it will land heads up on your next throw?
Answer: 50/50 (The previous tosses don’t make any difference; you always have an equal chance of heads or tails.)
33. You’re visiting a clothing store that has a strange way of pricing items. A vest costs $20, socks cost $25, a tie costs $15, and a blouse costs $30. You want to buy some underwear. How much will it cost?
Answer: $45. Items cost $5 for each letter used to spell the word.
34. How can you make this equation correct: 81 x 9 = 801?
Answer: Turn it upside down: 108 = 6 x 18.
35. You’re planning to spend your birthday money taking some friends to the movies. Is it cheaper to take 1 friend to the movies twice or 2 friends to the movies at the same time?
Answer: Take 2 friends at the same time, so you’ll only buy 3 tickets total. If you take 1 friend twice, you’ll need to buy yourself a ticket each time, for a total of 4 tickets.
36. Each day, a snail climbs 3 feet up a wall, but each night it slips 2 feet back down while it sleeps. If the wall is 30 feet high, how many days will it take for the snail to reach the top?
Answer: 28 days. Each day, the snail makes a 1 foot gain, bringing it to 27 feet by the 27th day. On the 28th day, it will climb the last 3 feet and reach the top.
37. Divide 40 by half and add 10. What’s the result?
Answer: 90. The instruction says to divide by half, not to divide in half. In other words, the equation is 40 ÷ .5 = 80 + 10 = 90.
38. Add me to myself and multiply by 4. Divide me by 8 and you will have me once more. What number am I?
Answer: This works for any number!
39. Lin is four times as old as her daughter Rosa. In 20 years, Lin will be twice as old as her daughter. How old are Lin and Rosa now?
Answer: Lin is 40, and Rosa is 10.
40. A box holds 13 blue marbles, 13 red marbles, and 13 green marbles. If you’re unable to see into the box, what is the minimum number of marbles you need to take out to ensure you have one of every color?
Answer: 27. You might need to take out every one of two colors of marbles (26) before pulling one of the third color (+1).
41. A store is offering a bat and ball for a total of $1.10. The bat costs $1 more than the ball. How much does each item cost separately?
Answer: The ball costs 5 cents, and the bat costs $1.05.
42. Find two numbers whose squares add up to 100. (Neither number is zero.)
Answer: 8 and 6 (64 + 36 = 100).
43. Miguel, Sara, and Olive share a box of 120 M&Ms. Miguel eats half the candy, Sara eats one-third, and Olive eats one-tenth. How many M&Ms are left?
Answer: 8. Miguel eats 60, Sara eats 40, and Olive eats 12. This leaves 8 pieces of candy uneaten.
44. What is unique about this number: 8,549,176,320?
Answer: When spelled out as words, it contains the numbers 0 to 10 in alphabetical order. (Eight, five, four, etc.)
45. Arrange the numbers 1 to 9 in a 3 x 3 grid such that the sum of each row, column, and diagonal is the same.
Answer: Row One: 8 3 4, Row Two: 1 5 9, Row Three: 6 7 2.
46. A rectangle has a perimeter of 24 inches. If the length is twice the width, what are the dimensions of the rectangle?
Answer: Width = 4 inches, length = 8 inches.
47. I am a four-digit number (ABCD). When you multiply me by 4, the answer is the same four-digit number in reverse (DCBA). What number am I?
Answer: 2,178.
48. What is the next number in this series? 7,645 5,764 4,576 _______.
Answer: 6,457 (Move the final digit to the beginning each time.)
49. A triangle has three angles that are all square numbers. What are the angles of this triangle?
Answer: 16 degrees, 64 degrees, and 100 degrees.
50. What is the smallest whole number that, when written out in words, uses all the vowels exactly once?
Answer: Five thousand.
51. An old woman dies on her 24th birthday. How can that be?
She was born on February 29, in a leap year, which occurs once every four years. Consequently, 24 x 4 = 96.
52. Lorenzo was born in 1988. In 1968, he was 20 years old. How could that be?
Lorenzo was born in 1988 B.C.E. So, we count the time backward. 1968 B.C.E. is 20 years later than 1988 B.C.E.
53. It’s the longest side of the triangle, starting with H and ending with E. What is it?
Hypotenuse.
54. Figures with sides have it, but a circle doesn’t. What is it?
An angle.
55. I am an odd number. If you subtract 10 from me, you get 15. What number am I?
25 (25 – 10 = 15).
56. I am thinking of a number. If you add 5 to it and then multiply the result by 3, you get 24. What number am I thinking of?
3 (3 + 5 = 8, 8 x 3 = 24).
57. How can you make 45 using only 4?
Use fractions: 44 + 4/4 = 45 because 4/4 = 1.
58. I put three matches on a table. I ask you to add two matches to get 8. How can you do this?
You can make the Roman numeral eight: VIII.
59. William takes two from five and gets four. How does he do that?
He takes the letters F and E from FIVE and gets IV, which is Roman numeral four.
60. A farmer bought a rooster to sell eggs for 1 cent each. The rooster lays five eggs daily. How much will the farmer earn in a week?
Nothing because roosters don’t lay eggs.
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