37 puzzles with answers · tap one to see its answer
Math Riddles and Brain Teasers
Math riddles hide a simple calculation behind a story: ages, prices, speeds, counting, a little geometry and a little probability. These 37 need no more than school arithmetic, but most have a twist that catches people who rush, and every answer shows the working. They suit a classroom starter as well as a quiet coffee break.
Every puzzle was solved by a second reader who had not seen the answer, on November 9, 2026.
I'm a two-digit number whose digits add up to 11. If you swap my two digits, I grow by exactly 27. What number am I?
Answer: 47
Why: Swapping the digits changes a number by 9 times the gap between them, so the digits differ by 3. Two digits that add to 11 and differ by 3 are 4 and 7, and 74 is 27 more than 47.
A mother is three times as old as her son. In 14 years, she will be exactly twice as old as he is. How old is the son now?
Answer: 14 years old
Why: If the son is s, then 3s + 14 = 2(s + 14), which gives s = 14. Check: today they are 14 and 42, and in 14 years they will be 28 and 56.
A store raises the price of a $100 jacket by 20%, then puts it on sale at 20% off the new price. What is the sale price?
Answer: $96
Why: The raise takes it to $120, and 20% off $120 is $24, leaving $96. The discount is taken from a bigger price, so it removes more than the raise added.
You toss three fair coins at once. What is the chance that all three land the same side up?
Answer: 1/4
Why: Three coins can land 8 equally likely ways, and only 2 of them, all heads or all tails, match. That is 2 out of 8, or 1/4.
A square's perimeter, measured in centimeters, is the same number as its area in square centimeters. How long is each side?
Answer: 4 cm
Why: With side s, the perimeter is 4s and the area is s times s. They are equal when s = 4, giving a perimeter of 16 cm and an area of 16 square cm.
Divide 20 by one quarter, then add 5. What number do you get?
Answer: 85
Why: Dividing by a quarter is the same as multiplying by 4, so 20 divided by one quarter is 80, not 5. Adding 5 gives 85.
In 6 years, Tia will be three times as old as she was 6 years ago. How old is Tia now?
Answer: 12
Why: If Tia is t, then t + 6 = 3(t - 6), so 2t = 24 and t = 12. Six years ago she was 6, and in six years she will be 18, which is three times 6.
A movie starts at 7:50 p.m. and runs for 2 hours and 25 minutes. At what time does it end?
Answer: 10:15 p.m.
Why: Two hours after 7:50 is 9:50. Ten more minutes reaches 10:00, and the last 15 minutes bring it to 10:15 p.m.
A wall clock loses exactly 2 minutes every hour. It is set to the right time at noon. What time does the clock show when the real time is midnight?
Answer: 11:36
Why: From noon to midnight is 12 hours, and losing 2 minutes each hour puts the clock 24 minutes behind. Midnight minus 24 minutes is 11:36.
In a class of 30 students, 18 play soccer, 15 play basketball, and 5 play neither sport. How many students play both?
Answer: 8 students
Why: Since 5 play neither, 25 students play at least one sport. Adding 18 and 15 gives 33, which counts the students who play both twice, so 33 minus 25 means 8 play both.
A melon weighs 600 grams plus one third of its own weight. How much does the melon weigh?
Answer: 900 grams
Why: If 600 grams plus a third of the melon is the whole melon, then 600 grams must be the other two thirds. One third is 300 grams, so the melon weighs 900 grams.
In the Okafor family, each daughter has as many brothers as sisters, but each son has twice as many sisters as brothers. How many children are in the family?
Answer: 7 children (4 girls and 3 boys)
Why: A daughter doesn't count herself, so there is one more girl than there are boys. With b boys, a son has b + 1 sisters and b - 1 brothers, and b + 1 = 2(b - 1) gives b = 3: 3 boys and 4 girls.
Five bakers can frost five cakes in five minutes, each baker working on one cake. At the same pace, how many bakers are needed to frost 60 cakes in 10 minutes?
Answer: 30 bakers
Why: Each baker frosts one cake every 5 minutes, so in 10 minutes one baker finishes 2 cakes. Frosting 60 cakes takes 60 divided by 2, which is 30 bakers.
When an airport's moving walkway is switched off, Lena walks its length in 90 seconds. When it's running, she rides its length standing still in 60 seconds. How long does it take her to walk along it while it's running?
Answer: 36 seconds
Why: Each second, walking covers 1/90 of the length and the walkway covers 1/60. Together that's 2/180 plus 3/180, or 1/36 of the length per second, so the trip takes 36 seconds.
Jo cycles up a hill at 12 km/h and comes straight back down the same road at 36 km/h. What is Jo's average speed for the whole round trip?
Answer: 18 km/h
Why: Say the road is 36 km: the climb takes 3 hours and the descent 1 hour, so 72 km take 4 hours, an average of 18 km/h. It isn't 24 km/h because Jo spends far longer going slowly.
After a game, every player on a team high-fived every other player on the team exactly once, for 78 high-fives in all. How many players were on the team?
Answer: 13 players
Why: With n players there are n times (n minus 1) divided by 2 high-fives. 13 times 12 is 156, and half of that is 78.
A table tennis tournament starts with 53 players. Every match knocks out its loser, and some players get a bye when a round has an odd number of players. How many matches are played to crown the champion?
Answer: 52 matches
Why: Each match knocks out exactly one player, and byes knock out nobody. To go from 53 players down to 1 champion, 52 players must be knocked out, so there are 52 matches.
What is the smaller angle between the hour hand and the minute hand of a clock at 3:40?
Answer: 130 degrees
Why: The minute hand at 40 minutes points to 240 degrees from 12. The hour hand has moved two thirds of the way from 3 to 4, so it points to 110 degrees, and 240 minus 110 is 130.
You roll two fair six-sided dice. What is the chance that at least one of them shows a six?
Answer: 11/36
Why: The chance that neither die shows a six is 5/6 times 5/6, or 25/36. Everything else has at least one six, which is 11/36 (not 1/3, because double six is counted only once).
How many squares of any size can you find in a 4-by-4 grid of small squares?
Answer: 30 squares
Why: There are 16 squares of size 1, 9 of size 2, 4 of size 3 and 1 of size 4. That adds up to 30.
Five friends line up in a row for a photo, and two of them, Ana and Bea, insist on standing side by side. How many different line-ups are possible?
Answer: 48 line-ups
Why: Treat Ana and Bea as one block, so there are 4 things to arrange: 4 x 3 x 2 x 1 = 24 ways. The pair can stand as Ana-Bea or Bea-Ana, which doubles it to 48.
A grandmother is as many years old as her grandson is months old. Together, their ages add up to 65 years. How old is the grandmother?
Answer: 60 years old
Why: A year has 12 months, so the grandmother is 12 times as old as the grandson. Together they make 13 grandson-ages, so he is 65 / 13 = 5 and she is 60.
A video game's price drops from $80 to $60 in a sale. By what percent must the $60 price rise to get back to $80?
Answer: 33 1/3%
Why: The price has to climb $20, and $20 is one third of $60. One third is 33 1/3%, even though the drop was only 25% of the original $80.
A gecko sits at the bottom of a wall 10 meters tall. Each day it climbs 3 meters, and each night it slides back down 1 meter. On which day does it first reach the top?
Answer: The fifth day
Why: It gains 2 meters per full day and night, so it starts day 5 at 8 meters. That day's 3-meter climb takes it past the top before it can slide back.
A bag holds red and green marbles in the ratio 3 to 5. After you add 10 red marbles, the bag has equal numbers of red and green. How many marbles were in the bag at first?
Answer: 40 marbles
Why: Write the counts as 3k red and 5k green. Adding 10 red makes 3k + 10 = 5k, so k = 5: there were 15 red and 25 green, 40 marbles in all.
Walking up the stairs from the 1st floor to the 4th floor of a building takes 45 seconds. At the same pace, how long does it take to walk from the 1st floor to the 10th floor?
Answer: 135 seconds
Why: Going from floor 1 to floor 4 climbs only 3 flights, so each flight takes 15 seconds. Floor 1 to floor 10 is 9 flights, which takes 135 seconds (not 112.5, as you'd get by counting floors).
A drawer holds 3 red socks and 2 blue socks. You pull out 2 socks at random. What is the chance that they are the same color?
Answer: 2/5
Why: There are 10 equally likely pairs of socks. Three of them are two reds and one is the two blues, so 4 out of 10, or 2/5, match.
Starting at noon and counting noon itself, how many times do the hour hand and the minute hand of a clock point in exactly the same direction before midnight?
Answer: 11 times
Why: The minute hand gains one full lap on the hour hand every 12/11 of an hour, so the hands meet 11 times in 12 hours. They meet at noon and then about every 65.45 minutes, and the twelfth meeting would be midnight itself.
What is the greatest number of pieces you can cut a round pancake into with 5 straight cuts, if you can't move or stack the pieces between cuts?
Answer: 16 pieces
Why: Each new cut adds one more piece than the number of earlier cuts it crosses, so at best the five cuts add 1 + 2 + 3 + 4 + 5 = 15 pieces. Starting from 1 whole pancake, that makes 16.
A 4-by-4-by-4 cube is painted red on the outside, then cut into 64 small cubes. How many of the small cubes have red paint on exactly two faces?
Answer: 24 cubes
Why: Cubes with exactly two painted faces sit along the big cube's edges but not at its corners. Each of the 12 edges has 4 cubes, minus 2 corners, leaving 2 per edge, and 12 x 2 = 24.
Two friends 9 km apart start jogging toward each other, one at 7 km/h and the other at 11 km/h. At the same moment, their dog starts running back and forth between them at 18 km/h, turning around instantly each time it reaches one of them. How far has the dog run when the friends meet?
Answer: 9 km
Why: Forget the zigzags: the friends close the gap at 7 + 11 = 18 km/h, so they meet after half an hour. The dog runs the whole half hour at 18 km/h, which is 9 km.
A baker has a tray of cookies. Whenever she packs them into equal bags of any size from 2 up to 6 cookies, exactly 1 cookie is left over, but bags of 7 use them all up exactly. What is the smallest number of cookies she could have?
Answer: 301 cookies
Why: One less than the total must be a multiple of every number from 2 to 6, so the total is 1 more than a multiple of 60. Checking 61, 121, 181 and 241 fails, but 301 is 7 x 43.
Numbering the pages of a book, starting from page 1, takes 300 digits in all. How many pages does the book have?
Answer: 136 pages
Why: Pages 1 to 9 use 9 digits and pages 10 to 99 use 180 more, for 189. The remaining 111 digits cover 37 three-digit pages, 100 through 136.
A bag holds three coasters: one red on both sides, one white on both sides, and one red on one side and white on the other. You draw one at random and lay it on the table without seeing its bottom, and the top is red. What is the chance that the bottom is red too?
Answer: 2/3
Why: There are three red faces you could be looking at, all equally likely. Two of them belong to the red-red coaster, so the chance is 2/3, not 1/2.
A 20 kg crate of cucumbers is 99% water by weight. After a few days in the sun, they have dried out until they are 98% water. How much do the cucumbers weigh now?
Answer: 10 kg
Why: The non-water part, 1% of 20 kg, is 0.2 kg and doesn't dry away. At 98% water that 0.2 kg is 2% of the total, so the total is 10 kg.
A rope fits snugly around a giant ball along its widest circle. How much longer must the rope be so it can float exactly 1 meter above the surface all the way around?
Answer: 2π meters (about 6.28 m)
Why: A circle of radius r has length 2πr, so raising the radius by 1 meter adds exactly 2π meters. The size of the ball doesn't matter at all.
A post office sells only 5-cent and 7-cent stamps. What is the largest postage, in whole cents, that you can't make exactly with them?
Answer: 23 cents
Why: Every amount from 24 to 28 cents can be made (for example 24 = 7 + 7 + 5 + 5 and 26 = 7 + 7 + 7 + 5), and adding 5-cent stamps to those reaches every larger amount. But 23 can't be made: taking out zero to three 7-cent stamps leaves 23, 16, 9 or 2 cents, and none is a multiple of 5.