Math Riddles with Answers
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You don't need to love math to enjoy these. Most math riddles here need logic more than arithmetic. Each one is labeled by difficulty with the worked steps shown when you reveal the answer, so you can check your reasoning. Grab some paper if you want, then filter to the level you are after.
Math riddles where the number you want is found by working backwards
Every card on this page is a riddle rather than a quiz question, and 71 of the 78 put a number in front of you before they ask for anything. That number is rarely the one you are meant to report. Read the sentence for the relation it states, four times as old, one dollar more, doubling every day, then name the value you actually want and write the relation around it. The arithmetic comes last and it is usually small.
The working habit is to undo rather than to compute. A lake that is full on the final day was half covered one doubling earlier. Ten dollars at the end of a story survives one spend and one halving back to the start. When a card hands you two descriptions of a single hidden value, set them against each other and cancel whatever they share. When the numbers refuse to cooperate, check what the question is really about: 7 of these cards turn on the shape of a digit or the spelling of a name rather than its size.
The neighbouring pages do a different job. Math brain teasers mixes a handful of scored rounds into a much longer set, and sorts every card into Easy, Medium or Hard so you can take one tier at a time. The kids version keeps the arithmetic to one easy step and hides the whole difficulty in the reading. Here the arithmetic is assumed and the relation is what is buried.
- Riddle 41: most people say Ten cents. One dollar more names the gap between the two prices, not the price of the bat. Pay the ball a nickel and the bat a dollar and a nickel, and both stated facts hold at the same time.
- Riddle 25: most people say Twenty five. Dividing in half and dividing by a half pull in opposite directions. The second asks how many halves fit inside thirty, which is sixty, and the ten arrives only after that.
- Riddle 45: most people say Ninety eight kilograms. The share that changes is the water, so follow the kilogram of dry pulp that cannot evaporate. Once that fixed kilogram counts as two percent of the melon, the fruit has to be fifty.
- Riddle 71: most people say Sixty four squares. That total counts only the single cells. A two by two block is a square as well, and so is every larger block up to the whole board, so eight different widths get counted.
Name the value you are hunting, write down the relation the sentence gives it, and work backwards to that value before reaching for arithmetic.
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1. Two fathers and two sons went fishing. Each caught one fish, yet they brought home only three fish. How is that possible? Easy
Most people first say: Four people
Need a hint?
Count the people, not the roles.
Show answer
There were only three people. A grandfather, his son, and his grandson make two fathers and two sons.
The roles overlap: the man in the middle is both somebody's son and somebody's father, so four labels sit on three heads and three catches feed everyone.
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2. I am a number. Multiply me by any other number and the answer never changes. What am I? Easy
Most people first say: The number one
Need a hint?
I am worth nothing on my own.
Show answer
Zero. Any number times zero is always zero.
Read never changes as the product standing still, not the other factor surviving untouched. A factor of nothing flattens every result to the same value.
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3. Which three whole numbers give the same result whether you add them or multiply them? Easy
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1, 2 and 3. Both the sum and the product equal 6.
Multiplying usually outruns adding, and that habit is what to drop. Down among the smallest counting numbers the two operations stay neck and neck, so test 1, 2, 3 before reaching for algebra.
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4. A farmer has 17 sheep. All but 9 run away. How many sheep are left? Easy
Most people first say: Eight left in the field
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9. The phrase all but 9 means exactly 9 stayed behind.
Seventeen is bait for a subtraction. The wording hands you the leftover flock directly, so the herd total can be ignored once you notice which group the phrase counts.
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5. There are 4 apples in a basket and you take away 3. How many apples do you have? Easy
Most people first say: One apple
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3. You took them, so those are the ones you have.
Watch the subject of that last sentence. It asks about your hands, not the basket, and to take something is also to own it, so the three you carried off are the count.
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6. What comes next in this sequence: 2, 3, 5, 9, 17? Easy
Most people first say: Twenty five
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33. Each number is double the previous one minus 1.
Each gap doubles instead of holding steady, so the constant difference idea has to go. Sixteen is the next jump, which agrees with the shorter rule of doubling a term and dropping one.
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7. How many eggs can you put into an empty basket one meter wide? Easy
Most people first say: A dozen
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Only one. After the first egg the basket is no longer empty.
Empty is a condition, not a description of the container. The first egg cancels it, so the sentence can only ever be true about a single egg, and the stated width does no work at all.
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8. Two ducks walk in front of a duck, two ducks walk behind a duck, and one duck walks in the middle. What is the smallest number of ducks? Easy
Most people first say: Five ducks
Need a hint?
The same ducks can play more than one role.
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3. Three ducks in a single row satisfy all three descriptions at the same time.
Nothing says the three phrases describe separate birds. Let one duck count as both a leader and a follower and the row shrinks to its shortest possible length.
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9. Which number has exactly as many letters in its name as its own value? Easy
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Four. The word four is spelled with exactly four letters.
Stop treating the name as a label for a quantity and start counting its letters. Spell the candidates upward from one and the match turns up on the fourth try.
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10. When does 11 plus 2 equal 1? Easy
Most people first say: It never does
Need a hint?
Stop thinking in plain arithmetic and look at the wall.
Show answer
On a clock. Two hours after 11 o'clock it is 1 o'clock.
Plain counting has no ceiling, but a dial does. Adding hours on a face that resets at twelve carries you past the top and back to the bottom, which is why the total shrinks.
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11. What comes next in this sequence: 1, 4, 9, 16, 25? Easy
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36. These are the square numbers, and 6 times 6 is 36.
The differences grow by two each step, which is the fingerprint of a squares list. Count positions rather than gaps and the sixth term arrives without any addition.
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12. What is half of a half of a half of 8? Easy
Most people first say: The number four
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1. Halving 8 three times gives 4, then 2, then 1.
Three separate halvings sit in that sentence, not one. The word repeats, so the operation repeats: divide by two at every step and the value drops to an eighth of where it started.
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13. A rooster sits on the exact peak of a barn roof and lays an egg. Which side of the roof does the egg roll down? Easy
Most people first say: The east side
Need a hint?
Check who is doing the laying.
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Neither side. Roosters do not lay eggs.
Roof pitch and peak are scenery. Check which animal the first clause names: a male bird produces no egg, so neither slope ever gets anything to carry.
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14. Add up every whole number from 1 through 100. What total do you get? Easy
Most people first say: About five thousand
Need a hint?
Pair the smallest number with the largest and watch the pattern.
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5050. Pair 1 with 100, 2 with 99, and so on: fifty pairs that each add up to 101.
Reorder before you add. Folding the run end to end makes every couple total one hundred and one, and there are half a hundred couples, so a grind becomes one multiplication.
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15. What comes next in this sequence: 3, 6, 12, 24? Easy
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48. Each number is double the one before it.
Compare each term to the one before by division rather than subtraction. The ratio holds at two the whole way, which marks a geometric run instead of a counting one.
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16. Multiply me by 4, then subtract 6, and you get three times me. What number am I? Easy
Most people first say: The number eighteen
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6. Four times 6 is 24, minus 6 is 18, and 18 is three times 6.
Two recipes describe the same hidden value, so set them equal instead of guessing. Stripping three copies from each side leaves one copy standing against the leftover six.
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17. Which two whole numbers multiply together to make exactly 31? Easy
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1 and 31. It is a prime number, so no other pair of whole numbers works.
Hunt for factors and you run out fast. Nothing below its own square root divides this total evenly, which is what being prime means, so the pair has to include the value itself.
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18. How much dirt is in a hole that is 2 meters long, 2 meters wide and 2 meters deep? Easy
Most people first say: Eight cubic meters
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None. A hole is empty, that is what makes it a hole.
Three measurements invite a volume sum, but a hole is defined by what was carried away. Dig deeper and you get more absence, never more material.
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19. Multiply together every number on a telephone keypad. What do you get? Easy
Most people first say: A very large number
Need a hint?
Do not forget the bottom row.
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Zero. The keypad includes a 0, and anything multiplied by zero is zero.
The digits on those keys run from one to nine in your memory, yet the bottom row holds a tenth key. One zero in the chain drags the whole product down to nothing.
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20. I am thinking of a number. Triple it and add 12, and you get the same total as multiplying it by 5 and subtracting 4. What is my number? Medium
Most people first say: Thirty six
Need a hint?
The two totals match, so the extra 16 must equal two more copies of the number.
Show answer
8. Both recipes give 36, since 3 times 8 plus 12 equals 5 times 8 minus 4.
Both descriptions land on one total, so line them up and cancel. Tripling and multiplying by five differ by two copies of the value, and the sixteen of slack between the constants pins each copy at eight.
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21. A brick weighs one kilogram plus half a brick. How much does the whole brick weigh? Medium
Most people first say: One and a half kilograms
Need a hint?
Put half a brick on each side of the scale.
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Two kilograms. If half a brick weighs one kilogram, the whole brick weighs two.
Half a brick appears on both sides of the sentence. Take it off each side and the kilogram left over is exactly the other half, which sets the full weight.
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22. A patch of lily pads doubles in size every day and covers the whole lake in 48 days. On which day did it cover half the lake? Medium
Most people first say: Day 24
Need a hint?
Work backwards from the last day.
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Day 47. One more doubling turns half a lake into a full lake.
Halfway in time is not halfway in size when growth doubles. Rewind one step from a full lake and the surface halves, so the midpoint sits right next to the end.
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23. If 5 machines take 5 minutes to make 5 widgets, how long would 100 machines take to make 100 widgets? Medium
Most people first say: One hundred minutes
Need a hint?
Figure out how long one machine needs for one widget.
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5 minutes. Each machine makes one widget in 5 minutes, no matter how many machines run at once.
Scaling the machines does not scale the clock. Find what a single machine does alone, five minutes for one widget, and adding more machines only widens the batch.
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24. A tailor has a 30 meter roll of cloth and cuts off a 3 meter piece every day. On which day does she make her last cut? Medium
Most people first say: Day 10
Need a hint?
The last piece never needs a cut of its own.
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Day 9. The ninth cut splits the final 6 meters into two pieces, so there is nothing left to cut on day 10.
Ten pieces sound like ten cuts. The final length arrives already separated, because one slice through the middle of six meters delivers two pieces at once.
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25. Divide 30 by half and add 10. What do you get? Medium
Most people first say: Twenty five
Need a hint?
Dividing by a half is not the same as dividing in half.
Show answer
70. Dividing by a half doubles a number, so 30 becomes 60, plus 10 is 70.
Two readings sit in the same phrase. Dividing in half cuts a number down, while dividing by a half asks how many halves fit inside it, and twice as many do.
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26. Count upward from one. Which number is the first whose English name contains the letter a? Medium
Most people first say: One hundred and one
Need a hint?
You will be counting for quite a while.
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One thousand. Every number from 1 to 999 avoids the letter a completely.
Spelling, not size, decides this race. Every name built from the units, the teens, the tens and hundred dodges that vowel, and only the next place value brings it in.
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27. Which is bigger, six dozen dozen or half a dozen dozen? Medium
Most people first say: They are the same
Need a hint?
Turn each phrase into a multiplication before comparing.
Show answer
Six dozen dozen. That works out to 864, while half a dozen dozen is only 72.
Both phrases hide a multiplication sign. The first stacks six groups of a dozen dozens, the second only six dozens, so one climbs into the hundreds while the other stays small.
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28. Maya's purse holds twice as many dimes as quarters, and the coins add up to 90 cents. How many quarters does she have? Medium
Most people first say: Four dimes
Need a hint?
Group every quarter with its two dimes and price the bundle.
Show answer
Two. Each quarter travels with two dimes, and two of those 45 cent bundles make 90 cents.
Bundle the coins before you count them. Every quarter drags two dimes along, worth forty five cents together, and ninety splits into exactly two of those bundles.
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29. A snail climbs 3 meters up a 10 meter well each day and slips back 2 meters each night. How many days does it take to get out? Medium
Most people first say: Ten days
Need a hint?
The last day is different from all the others.
Show answer
8 days. It gains 1 meter per full day, and on day 8 it climbs from 7 meters to the top before the night slip.
A net gain of one meter per day suggests ten days, but the slip only matters if the snail is still inside at dusk. From seven meters a single morning climb clears the rim.
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30. How can half of nine be four? Medium
Most people first say: Four and a half
Need a hint?
Think in Roman numerals.
Show answer
Write nine as the Roman numeral IX and cut it in half horizontally. The top half reads IV, which is four.
Treat the number as a picture rather than a quantity. Written the Roman way it splits along a horizontal line, and the upper strip is a legal numeral on its own.
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31. A father is four times as old as his son. In 20 years he will only be twice as old. How old is the son now? Medium
Most people first say: Forty years old
Need a hint?
Try setting the son's age to a small round number.
Show answer
10. The father is 40, and in 20 years they will be 60 and 30, which fits both facts.
Both ages move together, which is the part that keeps people guessing. Write the father as four sons now, add twenty to each, and the second condition leaves two sons equal to twenty.
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32. In a strange pet shop a duck costs 9 dollars, a spider costs 36 dollars and a bee costs 27 dollars. How much does a cat cost? Medium
Most people first say: Twenty seven dollars
Need a hint?
Count the legs of each animal.
Show answer
18 dollars. The shop charges 4.50 per leg, and a cat has four legs.
Prices climbing 9, 27, 36 look like a money pattern, but the rule lives on the animals. Divide each price by how many legs the creature stands on and the same rate appears every time.
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33. A hen and a half lays an egg and a half in a day and a half. How many eggs do 9 hens lay in 9 days? Medium
Most people first say: Nine eggs
Need a hint?
First work out what a single hen does in a single day.
Show answer
54. One hen lays two thirds of an egg per day, so 9 hens times 9 days times two thirds gives 54.
Nine and nine match the hen and a half pattern, which tempts a straight copy. Reduce to one bird for one day first, two thirds of an egg, then multiply by both nines.
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34. Using eight 8s and nothing but addition, how do you make exactly 1000? Medium
Most people first say: There is no such sum
Need a hint?
Start with the biggest chunk you can build from 8s.
Show answer
888 + 88 + 8 + 8 + 8. Those five numbers use eight 8s and add up to exactly 1000.
Kept apart, eight of them reach only sixty four, so the goal looks out of range. The setup never bans writing two or three of them side by side, and 888 does most of the work at once.
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35. If 3 cats catch 3 mice in 3 minutes, how many cats are needed to catch 100 mice in 100 minutes? Medium
Most people first say: One hundred cats
Need a hint?
Work out the catch rate of a single cat.
Show answer
Still 3. Each cat catches one mouse every 3 minutes, so 3 cats catch about 100 mice in 100 minutes.
Matching the two hundreds feels like the answer, which is the reflex to resist. Work out one cat's rate, a mouse every three minutes, and the existing team already keeps up.
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36. I am a two digit number. My digits add up to 9, and if you reverse my digits I grow by exactly 27. What am I? Medium
Most people first say: Forty five
Need a hint?
The difference of 27 tells you the digits are 3 apart.
Show answer
36. Reversed it becomes 63, which is 27 more, and 3 plus 6 equals 9.
A digit swap moves a two digit number by nine times the distance between its digits, so a gain of twenty seven puts them three apart. Add the sum rule and one candidate is left.
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37. Take 1000 and add 40. Add another 1000. Add 30. Add 1000 again. Add 20. Add 1000 one more time. Add 10. What is the total? Medium
Most people first say: Five thousand
Need a hint?
Add the thousands and the small numbers separately.
Show answer
4100. Most people blurt out 5000 because the small additions feel like they build another thousand.
The four big jumps arrive in a rhythm that makes the small ones feel like another thousand. Total the thousands alone, then the ten, twenty, thirty and forty, which come to a single hundred.
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38. I doubled my money, spent 10 dollars, doubled what was left, spent 10 more and ended up with exactly 10 dollars. How much did I start with? Medium
Most people first say: Twenty dollars
Need a hint?
Undo each step in reverse order.
Show answer
10 dollars. Work backwards: 10 plus 10 is 20, halve it to 10, add 10 to get 20, halve it to 10.
Running the story forward needs a guess, running it backward needs none. Undo the last spend, then the last double, and repeat, and every step lands on the same round figure.
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39. A knockout tournament starts with 64 players, and one loss sends you home. How many matches decide the champion? Medium
Most people first say: Six rounds
Need a hint?
Count the losers instead of the rounds.
Show answer
63. Every match eliminates exactly one player, and 63 players must go home before a champion remains.
Rounds are the tempting thing to add up, and they change size every time. Count departures instead: one player leaves per match, and all but the winner must leave.
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40. In two years I will be twice as old as I was five years ago. How old am I now? Medium
Most people first say: Fourteen years old
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12. In two years I will be 14, which is double the 7 I was five years ago.
Two snapshots of the same person sit two years ahead and five years behind. Line them up as one sentence about today and the doubling forces a single age.
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41. A bat and a ball cost 1 dollar and 10 cents together. The bat costs exactly one dollar more than the ball. How much is the ball? Hard
Most people first say: Ten cents
Need a hint?
The obvious answer of 10 cents makes the difference only 90 cents.
Show answer
5 cents. Then the bat costs 1.05, which is exactly one dollar more.
One dollar more is a gap, not the bat's price. Give the ball a value, add a dollar for the bat, and the ten cents of slack has to split between the two.
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42. What comes next in this sequence: 1, 11, 21, 1211, 111221? Hard
Need a hint?
Say the previous number out loud, digit by digit.
Show answer
312211. Each term reads the previous one out loud, so three 1s, two 2s, one 1.
No sum connects these terms. Each line is a spoken description of the line above it, so read the digits in pairs of count and value to build the next one.
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43. Three friends pay 30 dollars for a room. The clerk refunds 5, the bellboy keeps 2 and hands each friend 1 back. The friends paid 27 and the bellboy has 2, which makes 29. Where did the missing dollar go? Hard
Most people first say: The bellboy stole it
Need a hint?
You should subtract the 2, not add it.
Show answer
There is no missing dollar. The 27 they paid already includes the bellboy's 2, so adding it again counts it twice.
The tally mixes two directions of money. Twenty seven already includes the tip, so the honest sum adds the three refunded coins instead of stacking the tip on top again.
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44. What is the smallest number that grows by 12 when you turn it upside down? Hard
Most people first say: Sixty nine
Need a hint?
Only some digits still look like digits upside down.
Show answer
86. Turned upside down it reads 98, which is exactly 12 more.
Only a few digits survive a turn, and 6 and 9 trade places while 0, 1 and 8 hold still. Walk the flippable pairs upward and the first gain of twelve shows up in the eighties.
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45. A 100 kg watermelon is 99 percent water. After a day in the sun it is only 98 percent water. What does it weigh now? Hard
Most people first say: Ninety eight kilograms
Need a hint?
Track the part that does not evaporate.
Show answer
50 kg. The 1 kg of dry matter must now make up 2 percent of the whole, so the whole is 50 kg.
Chase the solid, not the water. One kilogram of pulp never leaves, and when that kilogram counts as two percent of the fruit instead of one, the melon must be half its old weight.
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46. What was the most recent year in the past that reads the same when turned upside down? Hard
Most people first say: Nineteen ninety one
Need a hint?
Only 0, 1, 6, 8 and 9 survive the flip.
Show answer
1961. Flip the digits and they still read 1961.
A mirror reading is not the same as a rotation. Turning the page swaps 6 with 9 while 0, 1 and 8 stay themselves, and no later year in the twentieth or twenty first century passes that test.
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47. You have exactly 100 dollars and must buy exactly 100 animals. Cows cost 10 dollars, pigs cost 3 dollars and chickens cost 50 cents. What do you buy? Hard
Most people first say: Ten cows
Need a hint?
You will need a lot of chickens.
Show answer
5 cows, 1 pig and 94 chickens. That is exactly 100 animals for exactly 100 dollars.
Two conditions run at once, one on money and one on headcount, and cheap birds are what let both close. Half the budget buys the cows, three dollars covers the pig, and the rest goes fifty cents at a time.
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48. What is unusual about the number 8549176320? Hard
Need a hint?
Spell each digit out as a word.
Show answer
Its digits appear in alphabetical order: eight, five, four, nine, one, seven, six, three, two, zero.
Nothing about the size of this number is strange, the spelling is. Write each digit as a word and the ten words fall into dictionary order from front to back.
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49. A pizza is cut into 8 equal slices and you eat 3 of them. What fraction of the pizza is left? Easy
Most people first say: Three eighths
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5/8. Eating 3 of the 8 slices leaves 5 slices.
The question asks for the remainder, not the helping. Eight equal slices make the denominator, the three that left make the bite, and the rest keeps the same slice size.
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50. What number comes next in this sequence: 5, 10, 15, 20? Easy
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25. The pattern counts up by fives.
Read the jumps before the numbers. A step of five never varies here, the same rhythm as counting nickels, so the run just keeps going one step past twenty.
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51. If today is Wednesday, what day of the week will it be exactly one week from now? Easy
Show answer
Wednesday. Seven days is one full week, so the day repeats.
Weekday names repeat on a cycle of seven, so any multiple of seven lands you back where you started. The date changes while the label does not.
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52. How many sides does a triangle have added to how many sides a square has? Easy
Most people first say: Twelve sides
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7. A triangle has 3 sides and a square has 4.
Added to is the instruction, so this is a sum and not a product. Recall the two shapes separately, three edges and four, then join the counts.
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53. I am the only even number that is also prime. Which number am I? Easy
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2. Every other even number can be divided by 2, so it is not prime.
Primes need exactly two divisors. Every even number above this one also divides by two, which is a third divisor, so the column of evens collapses and one value survives.
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54. What number comes next in this sequence: 100, 90, 80, 70? Easy
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60. Each step subtracts 10.
Every step here removes a ten, which makes this a countdown rather than a pattern of digits. Keep subtracting and the tens place drops one more notch.
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55. A baker's dozen is 13. How many rolls are in two baker's dozens? Easy
Most people first say: Twenty four rolls
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26. Two times 13 is 26.
Two twelves feel right and come up two rolls short. The phrase names a group of thirteen, so double that unit rather than the ordinary dozen.
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56. A shirt sells for 20 dollars after a 20 percent discount. What was its original price? Medium
Most people first say: Twenty four dollars
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25 dollars. The sale price of 20 is 80 percent of the original.
Percent off applies to the price you are hunting for, not to the one on the tag. The sale figure is four fifths of the original, so divide rather than add the fifth back.
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57. Tom is 3 years older than Jerry, and their ages add up to 21. How old is Tom? Medium
Most people first say: Nine years old
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12. Jerry is 9 and Tom is 3 years older.
Strip the difference out before you split. Removing the three year gap leaves an even total to halve, then hand the gap back to the older of the pair.
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58. A train departs at 2:15 and arrives at 5:00 the same afternoon. How many minutes was the ride? Medium
Most people first say: Two hundred forty five
Show answer
165 minutes. That is 2 hours and 45 minutes.
Clock time is not decimal. Count the whole hours first, then the leftover three quarters of an hour, and convert each piece at sixty rather than at a hundred.
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59. Three pens and two pencils cost 13 dollars, and a single pen costs 3 dollars. How much is one pencil? Medium
Most people first say: Four dollars
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2 dollars. Three pens cost 9, leaving 4 dollars for two pencils.
Price the known items out of the bill first. Three pens eat nine dollars, the leftover covers a pair of pencils, and the question wants one of them rather than both.
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60. If 4 oranges cost 2 dollars, how many oranges can you buy with 10 dollars? Medium
Most people first say: Five oranges
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20. Each orange costs 50 cents.
Find the price of a single fruit before spending anything. Four for two dollars is fifty cents each, and the larger budget then divides cleanly by that unit price.
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61. Using only a 3 liter jug and a 5 liter jug, how do you measure exactly 4 liters? Hard
Most people first say: Only 3, 5 or 8 liters
Need a hint?
What is left in a jug after a pour counts too.
Show answer
Fill the 5, pour into the 3 to leave 2, empty the 3, move the 2 over, refill the 5, then top off the 3 which takes 1, leaving 4 in the big jug.
Jug sizes are not the only measures available. What stays behind after a pour is a new amount, and the two liter remainder is the lever that reaches the target.
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62. How many times does the digit 1 appear when you write out every number from 1 to 100? Hard
Most people first say: Twenty times
Need a hint?
Count digits, not the numbers that contain them.
Show answer
21. Ten times in the units place, ten in the tens place, and once in 100.
Count digit slots, not numbers that contain the digit. The units column supplies one per decade, the tens column supplies a solid run of ten, and the final three digit number adds a last one.
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63. Printing all the page numbers of a book used exactly 189 digits. How many pages does it have? Hard
Most people first say: Sixty three pages
Need a hint?
Pages with one digit and pages with two cost differently.
Show answer
99. Pages 1 to 9 use 9 digits and pages 10 to 99 use 180 more.
Digits are not pages, so a straight division misses. The first nine pages use nine digits, the 180 left over cover ninety more pages, each of which prints two digits.
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64. Two trains 100 miles apart race toward each other at 40 mph and 60 mph. A bird flies back and forth between them at 90 mph until they meet. How far does the bird fly? Hard
Most people first say: One hundred miles
Need a hint?
Find how long the chase lasts before tracking the bird.
Show answer
90 miles. The trains meet in one hour, so the bird flies for one hour.
The zigzag invites an endless series, and none of it is needed. Add the closing speeds to get one hour of chase time, then multiply that hour by the flier's own speed.
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65. In a room of just 23 people, is it more likely than not that two of them share a birthday? Hard
Most people first say: No, you need 183 people
Need a hint?
Count pairs of people, not people.
Show answer
Yes. The chance passes 50 percent at 23 people.
Intuition counts matches against one fixed birthday, which is the wrong pool. With everybody compared to everybody, a couple of hundred pairs exist in that room and the odds of a clash tip just over even.
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66. What is the last digit of 7 raised to the 100th power? Hard
Most people first say: The digit seven
Need a hint?
Write out the first four powers and watch the last digit.
Show answer
1. The last digits of powers of 7 cycle 7, 9, 3, 1.
Last digits of a power repeat on a short loop, here four long. Divide the exponent by that loop length and a remainder of zero parks you on the final entry.
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67. A farmer must ferry a fox, a chicken, and a bag of grain across a river one at a time. Alone, the fox eats the chicken and the chicken eats the grain. What does he take across first? Hard
Most people first say: The fox first
Need a hint?
One item is both a predator and a meal.
Show answer
The chicken. That leaves the fox and grain safely together.
Guard the middle of the chain, not the biggest animal. The bird is the one that both threatens and is threatened, so removing it first leaves a safe pairing on each bank.
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68. You flip a fair coin and it lands heads five times in a row. What is the chance the very next flip is heads? Hard
Most people first say: Less than half
Need a hint?
Does the coin know what it did before?
Show answer
One half. Each flip is independent of the ones before.
Coins keep no record of the run behind them. Streaks look meaningful to us, yet the machinery of a single toss resets to even odds every time it is thrown.
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69. Three switches downstairs each control one of three bulbs upstairs, and you may climb up only once. How do you match every switch to its bulb? Hard
Most people first say: It cannot be done
Need a hint?
A bulb gives off more than light.
Show answer
Turn one on a while then off, turn a second on, and go up: lit is the second, warm and dark is the first, cold and dark is the third.
Light is only one signal a bulb gives. A lamp that burned for a while stays warm after the switch drops, so touch supplies the second clue the single trip seems to deny.
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70. A rope ladder hangs off a boat with rungs 30 cm apart, and 4 rungs sit underwater at low tide. The tide then rises 90 cm. How many rungs are underwater now? Hard
Most people first say: Seven rungs
Need a hint?
The ladder hangs from something that floats.
Show answer
Still 4. The boat floats up with the water, lifting the ladder too.
Nothing anchors the ladder to the seabed. A hull rises with the water it floats on, so the gap between the surface and the rungs above it never closes.
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71. How many squares of every size are there on a standard 8 by 8 chessboard? Hard
Most people first say: Sixty four squares
Need a hint?
Squares come in sizes from one cell to eight.
Show answer
204. It adds the square numbers 1, 4, 9, and so on up to 64.
A square here means any block of cells, not just the little dark and light ones. Count the placements for each width from one up to eight and add those counts together.
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72. If boiling one egg in a pot takes 6 minutes, how long does it take to boil three eggs together in the same pot? Hard
Most people first say: Eighteen minutes
Need a hint?
Do the eggs wait in line or share the heat?
Show answer
6 minutes. The eggs boil at the same time.
The count of eggs changes nothing about the water. All three sit in the same heat at the same moment, so the timer runs once rather than once per egg.
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73. A ball dropped from 16 meters bounces back to half its previous height each time. How far has it traveled the moment it lands for the third time? Hard
Most people first say: Twenty four meters
Need a hint?
The ball goes up as well as down.
Show answer
40 meters. Down 16, up 8, down 8, up 4, down 4.
Every rise counts as travel too, which is the half people leave out. Add the drop, then each bounce up and its matching fall, and stop the tally the instant the third landing happens.
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74. On a 12 hour digital clock, how many times in 12 hours does the display read the same forward and backward, like 12:21? Hard
Most people first say: Twelve times
Need a hint?
The hour digit has to match the last minute digit.
Show answer
57. Fifty four with single digit hours plus three more at 10, 11, and 12.
Only the hour digit and the final minute digit have to agree, which leaves the middle digit free to be anything under six. Nine hours times those six choices, plus three two digit hours that mirror themselves.
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75. You have 9 identical looking coins, but one is slightly lighter. Using only a balance scale, what is the fewest weighings that always finds the fake? Hard
Most people first say: Three weighings
Need a hint?
Three groups beat two.
Show answer
2. Split the coins into three groups of three.
Halving is the reflex, and thirds are faster. One weighing of three against three points to the light trio even when the pans balance, and the second finds the odd coin inside it.
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76. At a party everyone shakes hands with everyone else exactly once, making 45 handshakes in all. How many people were there? Hard
Most people first say: Forty five people
Need a hint?
Every pair shakes once, so each person is counted twice.
Show answer
10. Ten people make 45 different pairs.
Handshakes and guests are separate counts. Each pair meets once, so the total is every guest times one fewer, halved to stop counting each pair twice, and that shape hits forty five at ten.
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77. Two candles start the same length but one burns out in 4 hours and the other in 3 hours. After how long is the slower candle exactly twice as long as the faster one? Hard
Most people first say: Two hours exactly
Need a hint?
Track what is left of each candle, not what burned.
Show answer
2 hours and 24 minutes. That is twelve fifths of an hour.
Both candles shrink at steady but unequal rates, so write each remaining length as a fraction of the start. Setting one at double the other leaves twelve fifths of an hour on the clock.
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78. A car drives to a town at 30 mph and returns along the same road at 60 mph. What is its average speed for the round trip? Hard
Most people first say: Forty five miles per hour
Need a hint?
Which leg of the drive takes longer?
Show answer
40 mph. Average speed is total distance over total time, not the average of the two speeds.
Averaging the two numbers ignores how long each leg lasts. The slow half of the trip eats twice the time of the fast half, so the trip average leans toward the smaller speed.
Easy math riddles for kids
The arithmetic in a math riddle is rarely the hard part. It is a word problem with a trick hidden in its wording: the numbers stay small, and the real difficulty sits in how the question is phrased. Unlike a textbook exercise, the numbers rarely go beyond what you can hold in your head, so the work is noticing what the setup actually says. One classic on this page: a bat and a ball cost 1 dollar and 10 cents together, and the bat costs exactly one dollar more than the ball, so the ball is 5 cents rather than the 10 cents most people say first. Another asks how long a snail needs to escape a 10 meter well if it climbs 3 meters each day and slips back 2 meters each night. The answer is 8 days, because on the final day it reaches the top before the night slip happens. Read the setup twice before calculating.
Math riddles with answers for adults
The hen and a half problem still trips up engineers. Answers walk through the working, not just the number.
Number puzzles with hints
53 of the 78 riddles include a hint, so a wrong turn never has to end the run.
Your score
FAQ about Math Riddles with Answers
Do I need to be good at math to solve these?
No. Most math riddles here reward careful reading over calculation. If you can add and multiply small numbers, the rest is logic.
Why do most people answer 10 cents to the bat and ball riddle?
The wording invites plain subtraction: 1 dollar 10 cents minus 1 dollar leaves 10 cents. But then the bat costs 1 dollar and the ball 10 cents, a gap of only 90 cents. Splitting the leftover 10 cents evenly fixes it, giving 5 cents for the ball and 1.05 for the bat.
Are these math riddles good for school?
Teachers use them as warmups and early finisher tasks. They fit upper elementary through high school, and the hints let students help themselves when they get stuck.
Which of these can I solve without writing anything down?
The Easy tier is built for it, and so is most of the Medium tier. The Hard tier is where paper starts to pay: the page numbering card, the chessboard count and the candle pair all want a line of working.
If these numbers got your gears turning, try our math brain teasers with step-by-step answers for a fresh set of challenges. When the arithmetic stops being the hard part, the logic riddles drop the digits and leave you testing the one premise the question never stated.