Math Brain Teasers
These math brain teasers come with answers and a worked solution on every card. The grades run 25 Easy, 33 Medium and 26 Hard, and the grade chips above the list narrow the page to one tier at a time. Tap a card when you want to check your work.
Math brain teasers split between a missing fact and an assumption you added
Two jobs cover 55 of the 84 cards here. On 27 of them the block is a fact you either hold or do not: the interior angles of a pentagon, the trailing zeros in ten factorial, the count of squares of every size on a checkerboard. On 28 more nothing is missing at all, and the block is a condition you supplied while reading, such as the snail still slipping back on the day it reaches the top. Read the sentence once for what it states, then once for what you added.
The habit that pays is naming the quantity you actually want before touching a number. A handshake counted from both sides has to be halved. An average is a total in disguise, so four tests at eighty become three hundred twenty points and the fifth score falls out. When a card hands you a rate, shrink it to one hen, one typist or one minute first, then scale that up.
Two related pages do other work. The brain teasers shelf keeps every kind side by side, so a number puzzle sits next to a word one and no single reflex carries you through. On math riddles the sums stay small and the trick hides inside the sentence instead. Here you run the sum yourself, and ten of the cards score you as you answer.
- Riddle 17: most people say Eighty one eggs. Nine hens across nine days invites nine times nine. What scales is the rate, not the square: one hen manages an egg every day and a half, which is six eggs each across nine days, and nine of those is fifty four.
- Riddle 52: most people say Sixteen years old. Six years get added to each of them, so thirty already contains twelve years that have not happened yet. Subtract six once and sixteen appears. Subtract it twice, leaving eighteen to split between the two of them, and Sarah lands on twelve.
- Riddle 13: most people say Eleven socks. Eleven answers a different question, how many socks guarantee one of a named color, since ten of the other color can come out first. A pair needs no such worst case: with only two colors in the drawer, the third sock has to join one of the first two.
- Riddle 81: most people say The number 51. Fifty one really does shrink by thirty six when its digits swap, which is why the hunt tends to stop there. The card asks for the largest number that fits, and any digit pair four apart works, so nine and five beats five and one.
Say out loud what the card is really asking for, then decide whether you are missing a fact or carrying an assumption.
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1. Three consecutive whole numbers add up to 48. What are they? Easy
Most people first say: 16, 17, and 18
Need a hint?
The middle number is the average of all three.
Show answer
15, 16, and 17. Divide 48 by 3 to get the middle number, 16, then take one step down and one step up.
Dividing 48 by 3 hands you 16, and the pull is to start counting there: 16 plus 17 plus 18 overshoots to 51. The quotient is the middle step, not the first.
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2. In two years I will be twice as old as I was five years ago. How old am I? Medium
Most people first say: seven years old
Need a hint?
Write my age as x and turn the sentence into an equation.
Show answer
12. In two years I'll be 14, and five years ago I was 7. Set up x + 2 = 2(x - 5) and solve: x = 12.
Solvers grab the seven from five years ago and stop. Both phrases describe one person at different moments, so anchor the unknown at today and shift it forward and backward before comparing.
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3. A snail climbs a 10 meter wall. Each day it climbs 3 meters, and each night it slips back 2 meters. How many days does it need to reach the top? Medium
Most people first say: Ten days
Need a hint?
The snail does not slip back on the day it reaches the top.
Show answer
8 days. It gains 1 meter per full day, so after 7 days it sits at 7 meters. On day 8 it climbs 3 meters and reaches 10 before night falls.
Ten days comes from dividing the wall by the one meter the snail nets per cycle, a sum that bills it for a final slip that never happens. The last climb ends in daylight.
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4. What is half of two plus two? Easy
Most people first say: The number two
Need a hint?
Where you pause in the sentence changes the math.
Show answer
3. Read it as half of two, plus two. Half of 2 is 1, and 1 + 2 = 3.
Heard as one chunk the phrase becomes half of the total four, and solvers hand back 2. The words arrive in order, so the halving finishes before the second 2 shows up.
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5. A rope ladder hangs over the side of a ship with its rungs 30 cm apart. The tide rises 90 cm. How many rungs go under water? Medium
Most people first say: Three rungs
Need a hint?
Think about what the ladder is attached to.
Show answer
None. The ship floats, so it rises with the tide and the ladder rises too.
The 30 and the 90 beg to be divided for three rungs, and that picture has the ladder fixed to a pier that stays put. It hangs from a hull, which lifts as the water climbs.
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6. How can you take 1 away from 19 and get 20? Medium
Most people first say: You cannot do it
Need a hint?
Stop thinking in digits and start thinking in letters.
Show answer
Use Roman numerals. Take the I away from XIX and you're left with XX, which is 20.
In digits the subtraction only runs downward, 19 take away 1 leaves 18, so most readers declare it impossible and stop, never testing a notation where nineteen is three letters long.
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7. Using only addition, how do you add eight 8s to get 1000? Medium
Most people first say: It cannot be done
Need a hint?
You are allowed to glue 8s together into bigger numbers.
Show answer
888 + 88 + 8 + 8 + 8 = 1000. That uses exactly eight 8s.
Treat each 8 as a lone digit and all of them cap out at 64, nowhere near the goal, so the task reads as a trick with no solution. Nothing forbids parking two 8s side by side.
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8. A duck was given 9 dollars, a spider was given 36 dollars, and a bee was given 27 dollars. Based on this logic, how much money does a cat get? Medium
Need a hint?
Count the legs.
Show answer
18 dollars. Each animal gets 4.50 per leg. A duck has 2 legs, a spider 8, a bee 6, and a cat 4.
Nothing hangs on which animal it is. Nine over two legs, thirty six over eight, twenty seven over six all come to four fifty, and a cat walks on four of them.
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9. How many times do the hour and minute hands of a clock overlap in 24 hours? Medium
Most people first say: Twenty four times
Need a hint?
It is fewer than 24.
Show answer
22 times. They overlap 11 times every 12 hours, because the hands only meet about once every 65 minutes, not every hour.
Twenty four is one meeting per hour, counted straight off the dial. The minute hand needs roughly sixty five minutes to catch the drifting hour hand, so the eleven o'clock stretch of each half day holds none.
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10. If you multiply together every number on a phone keypad, what do you get? Easy
Most people first say: The product of one through nine
Need a hint?
Look at every key before you start multiplying.
Show answer
Zero. The keypad includes 0, and anything multiplied by zero is zero.
Solvers start at 1 and run up through 9 to 362,880, never dropping to the lone digit under the 7-8-9 row. That last digit flattens the whole line.
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11. I have two coins that add up to 30 cents. One of them is not a nickel. What are the coins? Medium
Most people first say: A quarter and a dime
Need a hint?
Read the sentence again. Only ONE coin is ruled out.
Show answer
A quarter and a nickel. One of them, the quarter, is not a nickel. The other one is.
Read as if neither coin were a nickel, the hunt starts with a quarter and a dime, which lands on 35 cents instead of 30. The sentence disqualifies exactly one of the pair.
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12. A grandfather clock takes 5 seconds to strike 6 o'clock. How long does it take to strike 12 o'clock? Medium
Most people first say: Ten seconds
Need a hint?
Time the gaps between strikes, not the strikes themselves.
Show answer
11 seconds. Six strikes have 5 gaps between them, so each gap is 1 second. Twelve strikes have 11 gaps.
Doubling the strikes doubles the time in most heads, giving ten seconds. The gaps are what you time, and twelve chimes hold eleven of them, one more than double the five inside six.
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13. A drawer holds 10 black socks and 10 white socks. The room is pitch dark. How many socks must you pull out to guarantee a matching pair? Easy
Most people first say: Eleven socks
Need a hint?
Imagine the worst possible luck on your first two picks.
Show answer
3. With only two colors, three socks always contain at least two of the same color.
Eleven comes from fearing a run of all ten blacks before a white appears, a worry aimed at collecting both colors rather than a match. Ten blacks in hand are already five pairs.
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14. Six coworkers each shake hands with every other person exactly once. How many handshakes happen? Medium
Most people first say: Thirty handshakes
Need a hint?
Be careful not to count the same handshake twice.
Show answer
15. Each of the 6 people shakes 5 hands, giving 30, but that counts every handshake twice. 30 divided by 2 is 15.
Thirty is six times the five hands one person grips, a tally that files your shake with me and my shake with you as two events. Any pair of coworkers shares one clasp.
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15. Which number increases by 12 when you turn it upside down? Medium
Most people first say: Ninety eight
Need a hint?
Only some digits still look like digits upside down: 0, 1, 6, 8, 9.
Show answer
86. Flip it and it reads 98, which is 12 more.
Ninety eight is the answer people hand back, but flip 98 and it reads 86, a drop of 12 rather than a gain. The rotation reorders the digits as well as turning the 6 into a 9.
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16. What three positive whole numbers give the same result whether you add them or multiply them? Easy
Most people first say: three twos
Need a hint?
Start small. Really small.
Show answer
1, 2, and 3. Added together they make 6. Multiplied together they also make 6.
Multiplication outruns addition once every factor reaches two, so three twos fail and one of the values has to be a one. That leaves a pair whose product beats their sum by exactly one.
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17. If a hen and a half lays an egg and a half in a day and a half, how many eggs do nine hens lay in nine days? Hard
Most people first say: Eighty one eggs
Need a hint?
First figure out what one hen does in one day and a half.
Show answer
54. One hen lays 1 egg in a day and a half, so each hen lays 6 eggs in nine days. Nine hens lay 9 times 6, which is 54.
Three matching halves look like they cancel, which is where eighty one comes from: one bird, one egg, one day. They do not cancel, so find the rate for a single bird over that stretch before scaling up.
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18. I am a three digit number. My tens digit is five more than my ones digit, and my hundreds digit is eight less than my tens digit. What number am I? Medium
Most people first say: The number 149
Need a hint?
Start with the tens digit. It has to be big enough to subtract 8 from.
Show answer
194. The tens digit must be 9 (so the hundreds digit can be 1), which makes the ones digit 4.
Five more is the pivot and it flips easily: in 149 the tens digit is 4 and the ones is 9, five more the wrong way round. Nothing under nine survives taking eight away, which is what pins the tens digit.
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19. Add me to myself, then multiply the result by 4. Divide that by 8 and you get me back again. What number am I? Medium
Most people first say: Only the number zero
Need a hint?
Try it with 3, then with 10. Notice anything?
Show answer
Any number at all. Doubling, multiplying by 4, then dividing by 8 brings every number back to itself: 2x times 4 is 8x, and 8x divided by 8 is x.
Zero gets tried first and survives the chain, so it looks like the one value that fits. Feed in 3 and it comes home too, which shows the chain returns whatever it is handed.
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20. You have a 3 liter jug, a 5 liter jug, and unlimited water. How do you measure exactly 4 liters? Hard
Most people first say: It cannot be measured
Need a hint?
Pouring from jug to jug is allowed. Track the leftovers.
Show answer
Fill the 5, pour into the 3, leaving 2 in the 5. Empty the 3 and pour the 2 in. Refill the 5 and top up the 3, which takes 1 liter. Exactly 4 liters remain in the 5.
Four is not a jug size and not the difference between the two, so the puzzle looks shut. The measuring tool is the empty liter left in a 3 jug already holding 2.
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21. How many times does the digit 9 appear when you write every number from 1 to 100? Medium
Most people first say: Ten times
Need a hint?
Count the ones place and the tens place separately. Don't forget 99 counts twice.
Show answer
20 times. It appears once in the ones place in each group of ten (9, 19, 29...) for 10 times, plus 10 more times in 90 through 99's tens place.
Ten comes from counting a single 9 in each decade and stopping there. The nineties add ten more in the tens place, 99 paying into both counts, which brings the total to 20.
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22. Two trains start 100 miles apart and drive toward each other, each at 50 mph. A bird flying 75 mph shuttles between them until they meet. How far does the bird fly? Medium
Most people first say: One hundred miles
Need a hint?
Ignore the zigzag. How long is the bird in the air?
Show answer
75 miles. The trains close at 100 mph, so they meet after exactly 1 hour. In that hour the bird flies 75 miles, no matter how many turns it makes.
A gap of one hundred miles sits between the trains, and it gets lifted off the page as the bird's total because the zigzag looks impossible to add up. The bird is airborne one hour, which caps it at 75.
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23. What number comes next in this sequence: 2, 3, 5, 9, 17? Medium
Most people first say: Thirty four
Need a hint?
Compare each number with double the one before it.
Show answer
33. Each term is double the previous one minus 1. 17 times 2 is 34, minus 1 is 33.
Doubling alone lands on thirty four, one past the mark, because every step also takes a single unit back off. The gaps say the same thing: one, two, four, eight, then a jump of sixteen.
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24. A book costs 1 dollar plus half its own price. How much does the book cost? Medium
Most people first say: One dollar fifty
Need a hint?
The 1 dollar must be the other half of the price.
Show answer
2 dollars. If half the price is 1 dollar, the full price is 2. Check: 1 + half of 2 = 2.
A dollar fifty is the quick answer, and it fails its own check: half of 1.50 is 75 cents, so the price would come to 1.75. The flat dollar has to be the missing half.
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25. There are three apples on the table and you take away two. How many apples do you have? Easy
Most people first say: One apple left
Need a hint?
Listen to the exact question being asked.
Show answer
Two. You took them, so now you have them. The question asks what YOU have, not what is left.
The subtraction runs on its own, 3 take 2 leaves 1, and that 1 answers a question nobody asked. Count what moved into your hands instead of what sits on the wood.
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26. What comes next in this strange sequence: 61, 52, 63, 94, 46? Hard
Most people first say: Eighty one
Need a hint?
Try reading each number in the mirror.
Show answer
18. These are the square numbers 16, 25, 36, 49, 64 written backwards. The next square is 81, which reversed is 18.
Eighty one is where most answers stop, the next square reported before the mirror step. Every entry here is a square written in reverse, so 81 flips to 18.
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27. Do this in your head: 1000 + 40 + 1000 + 30 + 1000 + 20 + 1000 + 10. What do you get? Medium
Show answer
4100
Most people blurt out 5000. The thousands add to 4000 and the small numbers add to 100, so the true total is 4100.
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28. What number comes next: 1, 1, 2, 3, 5, 8, ...? Easy
Show answer
13
The gaps look like a staircase, 1 then 2 then 3, promising a jump of 4 and the answer 12. That reading breaks at the front, where 1 and 1 sit a gap of zero apart. Adding the two previous terms gives 13.
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29. You cut a round pizza with 3 straight cuts that all cross at the center. How many slices do you get? Easy
Show answer
6
Doubling is the pull here: cut, cut, cut feels like 2 then 4 then 8. But each cut crosses the middle, so it is a diameter, and three diameters carve the circle into twice three wedges, six.
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30. What is half of a half of a half of 80? Easy
Show answer
10
Reading it aloud, most people lose count after two halvings and pick 20. The phrase stacks three separate halvings, so track how many times the word repeats, not the size of the leftover.
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31. What is the only number whose English spelling has its letters in alphabetical order? Hard
Most people first say: the word eight
Need a hint?
Write the number names out and compare their letters alphabetically.
Show answer
Forty
Walk each name letter by letter and stop at the first letter that falls earlier than the one before it. Eight dips at its g, one dips at its n, and every other name trips the same test.
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32. I am a two digit number. Reverse my digits and I grow by 27. My digits add up to 9. What number am I? Medium
Most people first say: The number 63
Show answer
36
The usual slip is handing back 63, the larger twin: reversed it shrinks by 27 rather than growing. Each swap moves a two digit number by nine times the digit gap, so the gap is 3.
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33. What is the smallest two digit prime number whose digits add up to 10? Medium
Most people first say: The number 37
Show answer
19
Which filter you run first decides this: starting from primes you happen to recall surfaces 37 or 73, while climbing the numbers whose digits add to 10 reaches 19 first, already prime and smaller than both.
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34. The sum of the first 10 odd numbers is 90. Medium
Show answer
False.
Sums of odd numbers from one always land on a perfect square, and 90 is not one, so the claim cannot hold. Ten of them stack into a ten by ten square, giving 100.
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35. Every odd number, spelled out in English, contains the letter E. Medium
Show answer
True.
Hunting for a counterexample among big numbers is wasted work, because only the last word matters, and one, three, five, seven and nine all carry an E. The teens from eleven to nineteen keep it too.
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36. Zero is an even number. Easy
Show answer
True.
Zero reads as nothing rather than a number, which is why it gets left out of even and odd altogether. The test does not change for it: two divides zero with nothing left over, and that is what even means.
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37. A father is 4 times as old as his son. In 20 years he will be only twice as old. How old is the son now? Medium
Most people first say: Five years old
Show answer
10. If the son is x, the father is 4x, so 4x + 20 = 2(x + 20), which gives x = 10.
Five comes from measuring the future father against his age today, 4x plus 20 equals 8x. The sentence compares him with his son twenty years on, so both ages carry the extra 20.
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38. If 5 machines take 5 minutes to make 5 widgets, how long do 100 machines take to make 100 widgets? Medium
Most people first say: One hundred minutes
Show answer
5 minutes. Each machine makes one widget in 5 minutes, so 100 machines make 100 widgets in the same 5 minutes.
A hundred minutes comes from scaling the clock by twenty alongside the count of machines and widgets. The newcomers work beside the original five, not behind them, so nobody waits in line.
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39. A bat and a ball cost 1.10 dollars together. The bat costs 1 dollar more than the ball. How much is the ball? Medium
Most people first say: Ten cents
Show answer
5 cents. The ball is 0.05 and the bat is 1.05, which is a dollar more and adds to 1.10.
Ten cents follows from pricing the bat at a flat dollar and handing over the change. Check the gap: 1.00 and 0.10 sit 90 cents apart, so the extra dollar comes off the top first.
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40. A patch of lily pads doubles its area every day and covers the whole pond on day 48. On what day was the pond half covered? Medium
Most people first say: Day twenty four
Show answer
Day 47. Since it doubles daily, the day before it is full it must be exactly half full.
Day twenty four is halving the calendar instead of the pond, and a doubling patch has nothing to do with the midpoint of the days. One step back from full is half.
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41. Counting every square of every size, how many squares are on a standard 8 by 8 checkerboard? Hard
Most people first say: the sixty four unit cells
Need a hint?
Count the one by one squares, then the two by two.
Show answer
204. You add the squares of 1 through 8, so 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 = 204.
Solvers count only the little cells and answer sixty four. A given size is pinned by its top left corner, which sits anywhere inside a shrinking window, seven by seven spots for size two, six by six for size three.
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42. What is the angle between the hour and minute hands of a clock at exactly 3:15? Medium
Most people first say: Zero degrees
Show answer
7.5 degrees. The minute hand points at 90 degrees while the hour hand has crept to 97.5 degrees.
Zero follows from parking both hands on the 3, the way the digits in 3:15 suggest. The hour hand crawls half a degree a minute, so fifteen minutes carry it 7.5 past the numeral.
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43. Pick any number, multiply it by 3, add 6, divide by 3, then subtract the number you started with. What do you always get? Medium
Most people first say: The number six
Show answer
2. The steps simplify to your number plus 2, and subtracting your number leaves just 2 every time.
Solvers who send only the tripled part through the division keep the six whole and answer six. The divide step hits that six as well, shrinking it to two, which is all that survives the final subtraction.
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44. In the song The Twelve Days of Christmas, how many gifts are given in total? Hard
Most people first say: seventy eight gifts
Need a hint?
Each day repeats every gift from the days before it.
Show answer
364. You add the running totals 1, 3, 6, 10 and so on up through day twelve, reaching 364.
Add one up to twelve and you get seventy eight, the usual miss. Each verse repeats all earlier presents and adds a fresh batch, so a day gives one up to its own number, and those stacked counts are summed.
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45. What is the greatest number of pieces you can get by cutting a flat pancake with just 3 straight cuts? Medium
Most people first say: Six pieces
Show answer
7. Each new cut crosses all the earlier ones, adding as many pieces as cuts it crosses plus one.
Six is the pizza answer, where every cut runs through one center point. Move the cuts off that point and each new one crosses every cut already there, adding one piece, then two, then three.
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46. A clock loses 5 minutes every hour. After 12 real hours pass, how far behind is it? Easy
Most people first say: fifty five minutes behind
Show answer
60 minutes. Losing 5 minutes each hour for 12 hours adds up to a full hour behind.
The loss is pegged to real hours, not to what the slow face shows. Solvers who count the dial's own eleven completed hours land on fifty five, while the true rate is five per genuine hour.
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47. Which weighs more, a kilogram of feathers or a kilogram of iron? Easy
Most people first say: the sack of iron
Show answer
They weigh the same. A kilogram is a kilogram no matter what the material is.
Heaviness of a substance is density, not mass, and the question already fixed the mass. Picture the volume instead, since the metal fills a small brick while the plumes need a room, which is what makes solvers pick the metal.
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48. What number comes next in this sequence: 2, 6, 12, 20, 30? Medium
Most people first say: The number forty
Show answer
42. The gaps grow by 2 each time, going 4, 6, 8, 10, then 12, so 30 + 12 = 42.
Forty appears when the last gap of ten is used twice, but the gaps widen by two each step: four, six, eight, ten, then twelve, lifting thirty to forty two.
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49. What is 40 divided by one half, then add 15? Medium
Most people first say: thirty five
Show answer
95. Dividing by one half doubles 40 to 80, and 80 + 15 = 95.
Division asks how many halves fit inside forty, and eighty of them do, so the count rises rather than falls. Solvers who read the phrase as cutting in half get twenty and finish at thirty five.
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50. A palindrome reads the same forwards and backwards. What is the smallest three digit palindrome? Easy
Most people first say: the number one hundred
Show answer
101. It reads the same both ways and is the first palindrome above 99.
Start at the floor of the range, where the leading digit must stay one, which forces the final digit to match it, so one hundred fails on its trailing zero. Only the middle slot is free, and zero is its cheapest choice.
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51. If 2 typists type 2 pages in 2 minutes, how many typists are needed to type 18 pages in 6 minutes? Medium
Most people first say: Eighteen typists
Show answer
6 typists. One typist types 3 pages in 6 minutes, so it takes 6 of them to reach 18 pages.
Pairing eighteen pages with eighteen typists ignores the clock, which also tripled from two minutes to six. One typist does a page every two minutes, so three pages each, and six typists cover eighteen.
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52. Sarah is twice as old as her brother. In 6 years the sum of their ages will be 30. How old is Sarah now? Medium
Most people first say: Sixteen years old
Show answer
12. Her brother is 6 and Sarah is 12, and in 6 years their ages of 12 and 18 add to 30.
Counting the six years once instead of twice gives three shares of eight and a Sarah of sixteen. Both siblings age, so twelve of the thirty is future, and the eighteen left splits two parts to one.
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53. You have a 15 cm stick and want to cut it into pieces that are each 3 cm long. How many cuts do you make? Easy
Most people first say: Five cuts
Show answer
4. Five pieces of 3 cm need only 4 cuts, since the last piece needs no cut after it.
Fifteen divided by three is five, and solvers hand that five straight back. Breaks fall only at the inner boundaries between neighbors, so five equal lengths need four of them, since the far end finishes on its own.
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54. Add up every whole number from 1 to 10. What is the total? Easy
Most people first say: The number 45
Need a hint?
Pair the smallest with the largest and count the pairs.
Show answer
55
Forty five is the sum of one through nine, which is what stopping a step early produces. Fold the list into five pairs that each make eleven, and the ten is inside one of them.
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55. What number comes next in this sequence: 3, 6, 9, 12? Easy
Need a hint?
These are the multiples of 3.
Show answer
15
Three into six looks like doubling, a read that breaks at nine. The step is a flat three every time, which is the three times table, so twelve goes to fifteen.
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56. A baker's dozen is how many items? Easy
Most people first say: twelve items
Show answer
13
Medieval bakers faced harsh penalties for selling light loaves, so they threw in a spare rather than risk a fine. The phrase is a trade custom, not arithmetic, which is why guessing the plain count misses.
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57. What is 7 times 8? Easy
Show answer
56
Squaring the wrong factor lands on forty nine or sixty four, and neither uses both numbers. Ten sevens minus two sevens is seventy less fourteen, which puts seven eights at fifty six.
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58. What is 25 percent of 80? Easy
Need a hint?
A quarter of a number is that number split into four equal parts.
Show answer
20
Twenty five is the percent, not the share, and repeating it back answers a different question. Cut eighty into four equal heaps and one heap, twenty, is the quarter asked for.
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59. What number comes next: 1, 2, 4, 8, 16? Easy
Need a hint?
Compare each number with double the one before it.
Show answer
32
The gaps run one, two, four, eight, so reusing eight gives twenty four. The gap doubles along with the terms, making the next jump sixteen and the next term thirty two.
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60. How many even numbers are there from 1 to 10? Easy
Most people first say: Four even numbers
Need a hint?
Do not forget that 10 counts too.
Show answer
5
Solvers who hear the range as single digits stop at nine and list two, four, six and eight, reporting four. Ten sits inside the range and is even itself, so it joins the list and makes five.
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61. How many degrees do the three angles of any triangle add up to? Easy
Most people first say: three hundred sixty degrees
Show answer
180 degrees
Picturing a full rotation around the shape is what produces three hundred sixty. Tear the three corners off a paper triangle and lay them together and they close into a straight line, which is half of that.
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62. What is half of 50? Easy
Show answer
25
One hundred is what doubling gives, not halving, and the two moves are easy to swap. Fifty comes apart into two matching shares of twenty five, which add back to fifty.
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63. What is 9 times 9? Easy
Show answer
81
Dropping two nines from ninety instead of one ends at seventy two, which is nine eights. Take ten nines, that is ninety, and remove a single nine to reach eighty one.
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64. What number comes next: 2, 4, 6, 8? Easy
Show answer
10
Nine is the next counting number, not the next even one, so the two patterns part ways here. Each step up this run adds two, which carries eight to ten.
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65. At a party everyone shook hands with everyone else exactly once, and there were 28 handshakes in all. How many people were there? Hard
Most people first say: Seven people
Need a hint?
The number of handshakes is people times one fewer, all divided by 2.
Show answer
8
Stacking one plus two on up to seven reaches twenty eight, and solvers read that last rung as the crowd. Each rung counts the greetings one new arrival adds, so seven rungs mean eight guests.
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66. Work this out in order: 6 + 6 divided by 6 + 6 times 6 - 6. What do you get? Hard
Most people first say: The number 42
Need a hint?
Handle the division and multiplication before the addition and subtraction.
Show answer
37
Left to right the expression walks to forty two, which is why that number feels right. The division and the multiplication go first, turning it into six plus one plus thirty six minus six.
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67. A number plus 30 percent of itself equals 91. What is the number? Hard
Most people first say: sixty three point seven
Need a hint?
The number and its 30 percent together make 130 percent of it.
Show answer
70
A value plus three tenths of itself is thirteen tenths, so cut ninety one into thirteen equal shares of seven and keep ten of them. Peeling thirty percent off ninety one instead lands near sixty four.
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68. What number comes next: 1, 2, 6, 24, 120? Hard
Most people first say: The number 600
Need a hint?
See what you multiply each term by to reach the next one.
Show answer
720
Using five twice gives six hundred, and five was the multiplier already spent. Each step multiplies by one more than the step before, so one hundred twenty meets six and becomes seven hundred twenty.
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69. Two numbers add up to 20 and multiply to 96. What are the two numbers? Hard
Most people first say: Nine and eleven
Need a hint?
Try pairs that add to 20 and check their product.
Show answer
8 and 12
Nine and eleven sit closest to the even split of ten and ten, and they multiply to ninety nine, three too many. Stepping one more pair apart gives eight and twelve, whose product is ninety six.
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70. A 50 dollar shirt goes up 10 percent one week, then drops 10 percent the next. What is the final price? Hard
Most people first say: Fifty dollars
Need a hint?
The second 10 percent is a percent of a bigger price.
Show answer
49.50 dollars
Fifty dollars assumes the two ten percents cancel, but each one is a percent of the price at that moment. The rise is ten percent of 50 and the fall is ten percent of 55, which is 50 cents more.
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71. A train 200 meters long moves at 20 meters per second. How long does it take to pass completely through a 300 meter tunnel? Hard
Most people first say: Fifteen seconds
Need a hint?
The train is not clear until its tail leaves the tunnel.
Show answer
25 seconds
Fifteen seconds measures just the tunnel, three hundred meters at twenty a second. Passing completely means the back end clears too, so the trip is five hundred meters and takes twenty five.
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72. What is the angle between the hour and minute hands of a clock at exactly 2:30? Hard
Most people first say: Ninety degrees
Need a hint?
By 2:30 the hour hand has moved halfway from 2 toward 3.
Show answer
105 degrees
Ninety degrees treats the hour hand as if it reached the three, and one hundred twenty leaves it parked on the two. Halfway between puts it at seventy five, which is one hundred five short of the minute hand.
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73. A jar of marbles doubles in number every minute and is full at minute 10. At which minute was it exactly a quarter full? Hard
Most people first say: Minute five
Need a hint?
A quarter full is two doublings before full.
Show answer
Minute 8
Halving the clock gives minute five, and that answers a different question: five is where half the time has gone, not where a quarter of the jar sits. Each halving of the marbles costs one minute, so nine is half and eight is a quarter.
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74. Your average across 4 tests is 80. What must you score on the 5th test to raise your average to 82? Hard
Most people first say: A score of 84
Need a hint?
Work with total points, not the averages.
Show answer
90
Nudging the target up by the two point rise gives eighty four, but that only lifts the average to 80.8. Five tests at eighty two need four hundred ten points and four tests gave three hundred twenty.
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75. The product of my age and the age I will be on my next birthday is 156. How old am I now? Hard
Most people first say: thirteen years old
Need a hint?
You are looking for two numbers in a row.
Show answer
12
Two neighbors multiply to roughly the square of whatever sits between them, so take the square root, about twelve and a half, and test the pair straddling it. Naming the next birthday age instead gives thirteen.
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76. Three consecutive even numbers multiply together to make 960. What are they? Hard
Most people first say: 6, 8, and 10
Need a hint?
Estimate the cube root of 960 to find the middle number.
Show answer
8, 10, and 12
Six, eight and ten multiply to four hundred eighty, exactly half of what is needed. Shift the whole trio up one even step and eight, ten and twelve reach nine hundred sixty.
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77. In a class of 30 students, 18 play soccer and 15 play basketball, and everyone plays at least one sport. How many play both? Hard
Most people first say: Twelve students
Need a hint?
The two groups add up to more than the class, and the extra is the overlap.
Show answer
3
Twelve comes from taking the 18 soccer players out of the 30, which counts who is left rather than who sits in both lists. The two rosters together name 33 students for 30 seats, and the three extra names are the doubles.
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78. What number comes next: 1, 3, 7, 15, 31? Hard
Need a hint?
Double each term and add one.
Show answer
63
Doubling alone stops at sixty two and misses the plus one that every step carries. Each term is twice the one before plus one, so thirty one becomes sixty three.
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79. How many zeros are at the end of 10 factorial, the product of every whole number from 1 to 10? Hard
Most people first say: Just one zero
Need a hint?
Count how many factors of 5 appear in the product.
Show answer
2
One zero is what counting the ten alone gives. The five also pairs with an even number to build a second ten, so the product closes with two zeros.
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80. It takes 6 painters 4 days to paint a house. At the same pace, how many days would 8 painters need? Hard
Need a hint?
Count the total painter-days the job requires.
Show answer
3 days
Four days belongs to the crew of six, not to the house, so quoting it again for a bigger crew is the slip. The house is twenty four painter days, and eight hands clear that in three.
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81. Reversing the digits of a two digit number makes it 36 smaller, and the two digits differ by 4. What is the largest number that fits? Hard
Most people first say: The number 51
Need a hint?
Reversing a two digit number changes it by 9 times the difference of its digits.
Show answer
95
Reversing shifts a two digit number by nine times the gap between its digits, so a gap of four satisfies both numeric clues and several pairs qualify. A hunt stops at the first; the word largest is what picks ninety five.
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82. What do all the interior angles of a five sided pentagon add up to? Hard
Most people first say: Three hundred sixty degrees
Need a hint?
Split the pentagon into triangles from one corner.
Show answer
540 degrees
Three hundred sixty is the four sided total and the full turn around a point, which is why it gets borrowed here. A fifth side adds one more triangle, pushing the total to five hundred forty.
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83. Two ordinary dice are rolled. In how many different ways can they add up to 7? Hard
Most people first say: Three ways
Need a hint?
The two dice are different, so order counts.
Show answer
6
Three ways counts one and six, two and five, three and four, treating the two dice as the same. They are separate, so each pair can land either way around, which doubles it to six.
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84. A car drives 60 miles at 30 mph, then another 60 miles at 60 mph. What is its average speed for the whole trip? Hard
Most people first say: Forty five mph
Need a hint?
Average speed is total distance over total time, not the average of the speeds.
Show answer
40 mph
Solvers split the difference between the two rates and answer forty five, which would hold only if equal time went to each leg. The slow 60 miles cost two hours against the fast one, giving three hours for 120 miles.
Easy math brain teasers to warm up
Half of two plus two comes apart the moment you hear where the speaker pauses, the apples question counts what you carried off and not what stays on the table, and a phone keypad hides a zero that flattens the whole product. Those three sit in the Easy grade, next to plain sums like 25 percent of 80 and nine times nine. Tap the Easy chip to read this grade by itself.
Hard math brain teasers with answers
A hen and a half laying an egg and a half in a day and a half, every square of every size on a checkerboard, a two digit number that shrinks by 36 when its digits swap: these three carry the Hard grade, which covers 26 of the 84 cards. Tapping a card opens the answer and the working together.
Math quiz rounds: multiple choice, type-in, true or false
Ten cards are scored as you play: four multiple choice rounds, three type the number boxes and three true or false calls. The other 74 reveal their answer when you tap them.
Your score
FAQ about Math Brain Teasers
Do I need strong math skills to solve these brain teasers?
No. Nothing on this page needs more than pencil arithmetic, and every card that uses algebra reduces to a single unknown. Two of the longer jobs are addition chains: eight square numbers total 204 on the checkerboard card, and twelve running totals reach 364 in the Twelve Days card. Other cards block you with a fact instead, such as the trailing zeros in ten factorial, or with a condition you supplied while reading and never checked.
If the tide rises 90 cm, how many rungs of a ship rope ladder go under water?
None. The 30 cm spacing and the 90 cm rise invite the division that gives three, and three is the answer people hand over. A ship is not fixed to the seabed: it floats up with the water, the ladder rises with the hull, and the waterline meets the rung it met before.
Are math brain teasers good for the classroom?
Yes. They work as bell ringers and warmups, and the ten scored cards mark themselves, so those need no answer key. Grade five and up can take on the Easy and Medium grades, while the Hard grade suits a math club or an adult table.
How many of these brain teasers come with a hint?
54 of the 84 cards carry a hint, tucked into a reveal of its own that sits above the answer, and every card in the Hard grade has one. A hint points at the first step or at the assumption to drop, so opening it leaves the answer shut.
Still in the mood for numbers? Our clever math riddles that make numbers fun keep the arithmetic small and bury the work in the wording. And when you want the same puzzling with letters instead of digits, dive into our word brain teasers, where the answer is built out of spelling rather than a sum.