162 Logic Puzzles & Brain Teasers With Answers
Brain teasers sit between a riddle and a puzzle: there is no pun to spot, but there is a chain of deduction to follow, and it usually holds together only if you keep track of every step.
A pen helps. Many of these are best attacked by writing down what must be true, then what that forces to be true next. Every one here comes with the answer and the reasoning.
They are a good fit for anyone who finds pure wordplay riddles frustrating - here the information you need really is all on the page.
A doctor gives you three pills and tells you to take one every half an hour. How long will the pills last?
You take the first pill immediately, the second after 30 minutes, and the third after another 30 minutes, a total span of one hour, not three half-hours.
Some adults still use these to count.
Many adults still count on their fingers, even though it's often thought of as a childhood habit.
Sophie's mother had 2 sons and 1 daughter. The sons names were George and John. What was the daughter's name?
The riddle is about 'Sophie's mother,' so Sophie herself must be that daughter.
I run around the city, but I never move.
A city wall surrounds the whole city while staying completely stationary.
You are in a room with 3 monkeys. One monkey has a banana, one has a stick, and one has nothing. Who is the smartest primate?
Humans are primates too, and the riddle's trick is realizing the reader, standing in the room, outranks all three monkeys in intelligence.
Where is the ocean deepest?
This is a joke answer: no matter where you measure, the ocean is always deepest at its very bottom.
What's at the head of an elephant and at the tail of a squirrel?
Both 'ELephant' and 'squirr-EL' contain the letters 'EL' -- at the start of one word and the end of the other.
2 people in front of 2 people. 2 people behind 2 people, and 2 people beside 2 people. How many people are there?
Four people standing in a square arrangement satisfy all three conditions at once, since each pair is simultaneously in front of, behind, and beside another pair.
What word is that, which, deprived of its first letter, leaves you sick?
This relies on an old, loose pun: removing the first letter from 'MUSIC' leaves 'USIC,' which said aloud sounds a bit like 'you sick' (as in 'are you sick?'). It's a stretch of wordplay rather than an exact letter-for-letter fit.
Besides Paris, what is the capital of France?
This is a play on words: the 'capital' (first, capitalized letter) of the word 'France' is F.
What part of a fish weighs most?
This is a pun: a fish's 'scales' are what you'd use to weigh it, since 'scales' also means a weighing instrument.
What was was, before was was was?
This wordplay riddle points out that the past-tense word "was" used to be the present-tense word "is" before events became past.
I you were to take two apples from three apples, how many would you have?
You physically took 2 apples, so you now have 2 in your hand, regardless of how many remain elsewhere.
What is round on both ends and hi in the middle?
Spelled out, "Ohio" is round letters (O) on both ends with "hi" sitting right in the middle.
Where can you add 2 to 11 and get 1?
On a 12-hour clock face, 11 o'clock plus 2 hours wraps around back to 1 o'clock.
If it has a quart capacity, how many pennies can you put into a empty piggy bank?
This is a trick riddle, not a math problem: you can put in only one penny, because after that the piggy bank is no longer "empty."
What is between heaven and earth?
In the phrase 'heaven AND earth,' the word 'and' is literally positioned between the two words.
A farmer has 17 sheep and all but 9 run away. How many are left?
"All but 9" means 9 sheep stayed behind and did not run away, so nine remain.
How can the letters OWONDER be rearranged to make one word?
OWONDER rearranges, letter for letter, into the phrase "ONE WORD" -- the answer is also the method for solving it.
John's mom had three children. The first child was April. The second child was May. What was the third Child's name?
The riddle names 'John's mom,' so naturally the third child being asked about is John himself.
What is the largest living ant on earth?
Hidden inside the word 'elephant' is the word 'ant,' and elephants are famously enormous.
What has three feet but no arms or legs?
A yard is a unit of length equal to exactly three feet, though it has no literal arms or legs.
What follows a dog wherever it goes?
A dog's tail is physically attached to it, so it trails behind the dog no matter where it goes.
What is never eaten before lunch?
Dinner is the meal that comes after lunch, so by definition it is never eaten before it -- a simple sequence riddle rather than wordplay.
I met a man and drew his name. He tipped his hat and played my game. What is his name?
This is a pun on 'and drew,' hidden inside the sentence itself, spelling the name 'Andrew.'
If you were standing directly on Antarctica's South Pole facing north, which direction would you travel if you took one step backward?
At the South Pole, every direction you face or move is technically north, since it's the southernmost point on Earth -- so even a "backward" step still takes you north.
Feed me and I live, yet give me a drink and I die. What am I?
Feeding fire with fuel keeps it burning ('alive'), but pouring water on it ('a drink') extinguishes it -- a rephrased version of an earlier fire riddle.
What's higher than the king?
A king's crown physically sits above his head, making it 'higher' than the king himself.
Look at me one way and I weigh a whole lot; turn me around and you'll see that I am not. What am I?
The word "ton" (a heavy unit of weight) spelled backward is "not," meaning something that isn't heavy at all -- a clever visual/word trick.
I turn around once. What is out will not get in. I turn around again. What is in will not get out. What am I?
Turning a key one way locks a door (keeping intruders out); turning it back the other way unlocks it (letting whoever's inside back out).
The sun bakes them, The hand breaks them, The foot treads them, The mouth tastes them.
Grapes ripen in the sun, are picked by hand, were traditionally crushed underfoot in winemaking, and are also eaten and tasted directly.
What breaks on the water but never on the land?
Ocean waves crest and "break" on the water's surface, but this specific kind of breaking doesn't occur on dry land.
What can you keep after giving it to someone?
Giving someone 'your word' (a promise) doesn't mean you lose it -- you still keep your word by honoring the commitment.
There is a boat with a ladder attached to it, the ladder is eight feet tall. If the water rises four feet how much of the ladder will be on top of the water?
Since the ladder is attached to the floating boat, it rises with the water level, so the entire eight-foot ladder stays above the water regardless of the tide.
Susan and Lisa decided to play tennis against each other. They bet $1 on each game they played. Susan won three bets and Lisa won $5. How many games did they play?
If Susan won 3 games and Lisa's net winnings were $5, Lisa must have won 8 games (8 - 3 = $5 net), so together they played 3 + 8 = 11 games.
What is so delicate that even mentioning it breaks it?
The word 'silence' is broken the instant you speak it out loud -- saying it defeats the very thing it names.
There is a clerk at the butcher shop, he is five feet ten inches tall, and he wears size 13 sneakers. What does he weigh?
A butcher shop clerk weighs meat for customers, so the physical details about the clerk himself are just a distraction.
What would you father's only sister's sister-in-law be to you?
Working through the family relations, a father's only sister's sister-in-law circles back to being your own mother.
Timmy's mother has three children. The first was named April. The next was named May. What is the final one's name?
The riddle names 'Timmy's mother,' so the third child sharing that family is simply Timmy himself.
George, Helen, and Steve are drinking coffee. Bert, Karen, and Dave are drinking soda. Is Elizabeth drinking coffee or soda?
George, Helen, and Steve (the coffee drinkers) each have the letter "e" appearing twice in their names, matching Elizabeth's name, which also contains two "e"s -- so she is drinking coffee too.
MT_TF_S What are the missing letters? Why?
The letters given (M, T, _, T, F, _, S) are the first letters of the seven days of the week, with Wednesday's W and Sunday's S missing from the blanks.
A mother had five boys Marco, Tucker, Webster and Thomas. Was the fifth boys name Frank, Evan or Alex?
Look at just the first letters of each brother's name to spot the days-of-the-week pattern.
What gets broken without being hold?
A promise is an intangible commitment; it can be "broken" (not honored) despite never being a physical object one holds.
There is a word in the English language in which the first two letters signify a male, the first three letters signify a female, the first four signify a great man, and the whole word, a great woman. What is the word?
"He" signifies a male, "Her" signifies a female, "Hero" signifies a great man, and the full word "Heroine" signifies a great woman -- each stage of the word builds in meaning exactly as described.
The more you take from me, the bigger I get. What am I?
Digging out (removing material from) a hole only makes the hole itself larger.
What's always coming, but never arrives?
"Tomorrow" is always one day ahead of today -- once it comes, it has become "today," so tomorrow itself never truly arrives.
If a rooster laid a white and brown egg, what kind of chicks would hatch?
Think about the literal properties of a 'nan'. The riddle uses metaphors to describe its physical form or function.
Homeless man bets he can sing a song about "Frederica Armstrong Miller."
Think about the literal properties of a '"happy birthday."'. The riddle uses metaphors to describe its physical form or function.
Payoff 2n (St. Petersburg). Charge to play?
The mathematical expectation is infinite, but most people wouldn't pay more than �20. This illustrates that humans value money based on 'utility' rather than just the raw expected amount.
Rule: Circle=Yellow. Cards: C, S, Y, R. Check?
You check the Circle (to see if back is Yellow) and the Red card (to see if front is a Circle, which would break the rule). Yellow and Square can't invalidate the rule.
Probability to be the last to try pitcher?
This is a property of a 'random walk' on a circle. Every person is equally likely to be the last one reached before the circle is completed.
Surprise test impossible logic?
If the test hasn't happened by Thursday, the students know it must be Friday (so it's not a surprise). This logic continues backward to Monday, 'proving' it can never be a surprise.
Sphere or Torus using rocks?
On a sphere, any two 'great circles' must intersect. On a torus, you can have a loop that goes around the center and another through the hole that never meet.
9 correct predictions in a row. Psychic?
The company sends 5,000 emails: 2,500 say Team A wins, 2,500 say Team B. They keep splitting the winners until one small group (like Kelly) has seen a perfect streak.
Describe a chicken in computer programming.
In coding, a function is something that takes an input and provides an output. Grain is the parameter, and the Egg is the return value.
Hourglass weigh more falling or at rest?
When sand is in the air, its weight isn't recorded by the scale. However, the force of the sand hitting the bottom is greater than its static weight, resulting in a net increase during the flow.
Pays payout in Yen. Charge to play?
The expected value is the average of all outcomes: (1+2+3+4+5+6)/6 = 21/6 = 3.5. To make a profit, the 'house' must charge more than the expected payout.
5 black spins. Is red "due"?
The roulette wheel has no memory. Each spin is a fresh event with the same probability (ignoring the green zero), regardless of what happened before.
10 pennies in 3 cups, each has odd number.
Put 1 in the first, 1 in the second, and 8 in the third... but wait, the trick is nesting. Put 1 in cup A, 2 in cup B, and nest B inside cup C (which has 7). Now C has 9 (odd).
Spoon tea into coffee, mix, spoon back. More what?
Since you started and ended with the same volume in each cup, any 'tea' that stayed in the coffee must have been replaced by an exactly equal volume of 'coffee' in the tea.
Max slices from 4 straight cuts?
The formula is (n^2 + n + 2) / 2. For n=4, that is (16 + 4 + 2) / 2 = 11. This assumes cuts can overlap and pass through previous cuts.
Ways to arrange 8 books on a shelf?
The number of permutations is n factorial (n!). For 8 books, it is 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320.
1 poisoned bottle in 1000. Prisoners needed?
Give each prisoner a unique combination of bottles to sip from based on binary (0 and 1). The specific combination of prisoners who get sick creates a binary code for the poisoned bottle number.
P1 (4 of kind), P2 (3 of kind). Worst possible hand?
If Player 1 has four of a kind and Player 2 has three of a kind, there must be at least three cards of the same rank on the shared board. Your hand will use those same three cards.
Break stick at 2 random points. Triangle prob?
Using the 'triangle inequality' theorem, no piece can be longer than 0.5m. Visualizing this on a 2D plot of possible break points shows the 'success' area is 1/4 of the total area.
Monkey climbs rope with matching weight. Weight?
The force the monkey exerts to climb increases the tension in the rope equally on both sides. Thus, both the monkey and the counterweight accelerate upward together.
Reverses left/right but not up/down?
If you point your finger to the right, the mirror image points to the right. The reversal is actually in the 'depth' (front to back) dimension relative to the mirror's surface.
Camel 3000 bananas, 1k km. Max reach?
The camel must leave 'caches' of bananas. To minimize the 'cost' of travel, he moves the bananas in stages until the total supply matches his max capacity for the remaining distance.
Get fair toss from biased coin.
If you toss twice, the probabilities of HT and TH are both (p * (1-p)). Since these are equal, assigning one to 'Heads' and the other to 'Tails' creates a fair 50/50 result.
Spheres with 6cm holes. Which has more volume?
The volume of a spherical ring depends only on the height of the hole (h). The formula V = (pi * h^3) / 6 shows the radius (R) of the original sphere cancels out.
200 fish, 99% Gold. Remove how many for 98%?
In 200 fish, 198 are gold (99%). To make them 98%, the 2 non-goldfish must represent 2% of the total. 2 is 2% of 100. So you must have 100 fish total (remove 100 gold).
Brothers Chris (FL) and Connor (OR) same time. How?
Florida has a tiny portion in Central Time, and Oregon has a portion in Mountain Time. During the DST 'fall back' hour, the times can align perfectly across the country.
Irrational number ^ irrational power = rational?
Consider x = sqrt(2)^sqrt(2). If x is rational, we are done. If x is irrational, then x^sqrt(2) = (sqrt(2)^sqrt(2))^sqrt(2) = sqrt(2)^2 = 2, which is rational.
1st sits random. Last gets assigned seat prob?
This is a classic probability puzzle. Either the first person takes your seat, or they take their own, or they take someone else's which triggers a chain that eventually hits yours or theirs.
Does washer hole expand or shrink when heated?
Thermal expansion is like a photographic enlargement. Every part of the object, including the 'empty' hole, expands proportionally.
How many barbershops are in the USA?
Estimate based on one barber per ~2,500 people. With a US population of 330 million, 130,000 is a standard Fermi estimation result.
100 cheating husbands. Execution day?
If there was 1 cheater, his wife would know immediately. If 2, they wait to see if the other wife acts. By the 100th day, the lack of action by others proves your own husband is one.
Truth 3/4 times. Says 6 on a die. Prob it's a 6?
The probability he says 6 AND it is 6 is (1/6 * 3/4). The probability he says 6 but it isn't 6 is (5/6 * 1/4). Use Bayes to find the ratio.
5 bandits split 100 coins. Senior proposal?
The senior bandit knows he only needs two other people to agree. He offers 1 coin to those who would get nothing in the next-best scenario to secure their vote.
Families stop childbearing after 1st boy. Sex ratio?
Every individual birth has a 50/50 chance. No matter the 'stopping rule,' the total expected number of boys and girls in the population will remain equal.
How many squares on an 8x8 chessboard?
Don't just count the 1x1 squares. You must sum all possible sizes: 1x1 (64), 2x2 (49), 3x3 (36), 4x4 (25), 5x5 (16), 6x6 (9), 7x7 (4), and 8x8 (1).
How many ping pong balls fill a 747?
Estimate the volume of a 747 (approx 1000 m^3) and the volume of a ping pong ball, then account for the 'packing fraction' of empty air space between balls.
C beats T by 10m in 100m. C starts 10m back. Winner?
Since Chandler runs 100m in the same time Toni runs 90m, when Chandler is 10m back, they will meet at the 90m mark. Chandler is faster and will pull ahead in the last 10m.
Does level change when ice in water melts?
According to Archimedes, the floating ice displaces a volume of water equal to its weight. When it melts, it becomes water of that exact weight and volume.
4 people: 1, 2, 5, 10 mins. Bridge (max 2). Min time?
Fastest pair (1&2) cross (2m), 1 returns (1m), slowest pair (5&10) cross (10m), 2 returns (2m), fastest pair (1&2) cross again (2m). 2+1+10+2+2 = 17m? Wait, logic says 15m is possible.
31 games in elimination tournament. Players?
In any knockout tournament, every player except the winner must lose exactly one game to be eliminated. If there were 31 games, 31 people lost.
3 doors: Heaven, 1-day Hell, 2-day Hell. Avg days?
E = 1/3(0) + 1/3(1+E) + 1/3(2+E). Solving for E: E = 1 + 2/3E -> 1/3E = 1 -> E = 3.
110m rope. 1ft slack added/pulled up. Truck fits?
Adding 1ft of slack to 110m (360ft) creates a triangle with base 180 and hypotenuse 180.5. sqrt(180.5^2 - 180^2) = 13.4 ft, plenty for a truck.
Which is greater: e? or ?e?
Take the e-th root of both. e^(1/e) is the maximum value for the function x^(1/x). Since e is the base of the maximum, e^pi > pi^e.
Surgeon with 2 gloves must operate on 3 patients. How?
Patient 1: Gloves A and B. Patient 2: Only Glove B (top one removed). Patient 3: Turn Glove A inside out and put it over B. A's clean side is now outside.
Duck in pond. Cat runs 4x faster on edge. Escape?
The duck swims in a circle of radius R/4. The cat has to run halfway around the pond (pi * R). The duck's distance is shorter than the cat's travel time allows for.
1/2 of 2/3 of 3/4... of 9/10 of 1,000?
The series is (1/2)*(2/3)*(3/4)*...*(9/10). The numerators and denominators cancel out diagonally, leaving 1/10. 1/10 * 1,000 = 100.
Pick 1 of 3. Empty removed. Do you switch?
Your initial pick had a 1/3 chance. The remaining 2/3 chance is now concentrated in the one unopened envelope the interviewer didn't discard.
Explain a database to an 8-year-old.
Use a metaphor of an organized filing system or library where everything has a specific label and 'shelf' to make it easy to find later.
Standard deviation of {1, 2, 3, 4, 5}?
The mean is 3. Squares of deviations: (1-3)^2=4, (2-3)^2=1, (3-3)^2=0, (4-3)^2=1, (5-3)^2=4. Average is 10/5 = 2. SD is sqrt(2) ? 1.414.
1/4 into tunnel. Meet train at start or end. Speed ratio?
If she meets the train at the end after running 3/4 of the way, and she would have met it at the start after running 1/4 back... set up the time/distance equations.
Sum of digits from 1 to 1,000,000?
The sum for 0-999,999 is (sum of digits 0-9) * (number of positions) * (frequency). 45 * 6 * 100,000 = 27,000,000. Add 1 for the '1' in 1,000,000.
Helium balloon in car accelerating forward. Direction?
In an accelerating car, heavier air is pushed to the back. This creates a pressure gradient that 'buoys' the lighter helium balloon toward the front.
HH = Jamie takes 2. Any other = Ashley takes 1. Winner?
There are 4 outcomes: HH, HT, TH, TT. HH (Jamie) happens 1/4. HT, TH, TT (Ashley) happen 3/4. Ashley wins 3 times for every 1 time Jamie wins (actually 3 coins to Jamie's 2).
100 ants on 1m stick at 1cm/s. Max time to clear?
Because all ants are identical, a 'bounce' is mathematically the same as two ants passing through each other. The max time is just the time for the furthest ant to walk to the end.
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