115 brain teasers with answers

You pass the runner currently in second place. Which place do you now hold?

Hint: You did not pass the leader.

One match is available beside a candle, a lantern, and a fireplace. What must be lit first?

Hint: What do you need before you can light anything at all?

A bus leaves at 9:35 a.m. and travels for 2 hours 45 minutes. What is its arrival time?

Hint: Add the 2 hours first, then the 45 minutes, and watch for noon.

Rearrange LISTEN into a word associated with quiet.

Hint: Use all six letters. A quiet room is...

Uma finishes before Rae, Rae before Sol, and Sol before Tia. Who finishes first?

Hint: Who is never said to finish after anyone?

Choose one of 3 shirts, one of 4 pairs of trousers, and one of 2 hats. How many outfits are possible?

Hint: Multiply the numbers of choices together.

An arithmetic sequence starts 7, 11, 15, 19. Continue it by one term.

Hint: Look at how much each number goes up by.

Socks come in four colors. Without looking, how many socks guarantee that two share a color?

Hint: Imagine the unluckiest draw: one sock of each color first.

The letters of EARTH can name a body organ. Name it.

Hint: It beats in your chest.

Dena is taller than Eli. Farah is shorter than Dena but taller than Eli. Order them from tallest to shortest.

Hint: Farah fits between the other two.

A recipe uses 240 grams of flour for 6 muffins. At the same rate, how much flour makes 15 muffins?

Hint: Work out the flour for one muffin first.

Supply the next term of the arithmetic sequence 42, 37, 32, 27.

Hint: Check the gap between neighboring numbers. Is it the same each time?

Thirteen people record only their birth month. What must be true?

Hint: There are only twelve months to go around.

Turn COLD into a precious metal by changing one letter.

Hint: Change the first letter.

Four lockers stand left to right. P is at the far left, Q is immediately right of P, and S is at the far right. Where is R?

Hint: Place the three named lockers first. One spot is left.

On a map, 3 centimeters represents 12 kilometers. What distance does 8 centimeters represent?

Hint: How many kilometers does 1 centimeter stand for?

Extend the geometric sequence 3, 9, 27, 81 by one term.

Hint: Each number is the one before it multiplied by the same amount.

Every amber token is round, and no round token is wooden. Could an amber token be wooden?

Hint: An amber token is round. What do we know about round tokens?

A one-letter change turns MOUSE into a building. Which word results?

Hint: Change the first letter to make somewhere people live.

Art, music, and science talks occur at 1, 2, and 3 o'clock, one per hour. Science is at 3, and art is before music. When is music?

Hint: Science takes 3 o'clock, which leaves 1 and 2.

Triple a number and add 4 to get 31. What is the number?

Hint: Take away the 4 first, then undo the tripling.

A geometric sequence with positive terms reads 160, 80, 40, 20. Which term is next?

Hint: Compare each number with the one before it. What happens every time?

Some poets are cyclists, and all cyclists wear helmets. What follows about the poets who are cyclists?

Hint: Follow the chain from poet-cyclist to cyclist to helmet.

Delete the first letter of PLANE to name a narrow road.

Hint: Think of a narrow country road.

A code replaces each letter with the next letter of the alphabet. Decode DBU.

Hint: Move each letter one place back in the alphabet.

A rectangle has perimeter 38 units and length 12 units. Find its width.

Hint: The two lengths use 24 units of the perimeter.

Starting with 2 and 3, each new term is the sum of the previous two. What follows 2, 3, 5, 8, 13?

Hint: Add the last two numbers together.

From TRAIN remove one letter to get precipitation.

Hint: It falls from clouds.

Box A contains the key to B, B contains the key to C, and C holds the prize. Which box must be opened first?

Hint: Which box can you open without a key from another box?

The base of a triangle is 14 units and its perpendicular height is 9 units. What is its area?

Hint: A triangle is half of a rectangle with the same base and height.

Advance three months at a time from February to May to August to November. Name the next month.

Hint: Count three months on from November, past the end of the year.

Insert one letter into PLAN to make a flying vehicle.

Hint: The new letter goes on the end.

A three-digit password has a first digit twice its second and a third digit one less than its second. The second digit is 3. What is the password?

Hint: The second digit is 3, so the first digit is twice 3.

A bag holds 5 red, 3 blue, and 2 green counters. What is the probability of drawing green once?

Hint: How many counters are green, out of how many in all?

Perfect squares begin 1, 4, 9, 16, 25. Supply the sixth term.

Hint: The fifth term is 5 times 5.

Which letter can be added to STAR to mean the beginning of something?

Hint: A race has one of these, and so does a film.

A meeting is after Monday but before Thursday, and it is not on Wednesday. Which day is it?

Hint: List the days between Monday and Thursday.

Reading the prime numbers in order gives 2, 3, 5, 7, 11. Which number follows?

Hint: Which number after 11 can be divided only by 1 and itself?

Tooth, hair, and paint share which following word?

Hint: You hold one in your hand for all three jobs.

Cubes appear in order as 1, 8, 27, 64. Name the next cube.

Hint: 64 is 4 times 4 times 4. Try 5.

An animal is hidden in eduCATION. Which one?

Hint: Look at the capital letters.

Decode alphabet positions 8-5-1-20 as a word.

Hint: 8 is H, the eighth letter.

Using A=1 through Z=26, what word is 13-1-16?

Hint: 13 is M, the thirteenth letter.

Rearrange BELOW to name a joint in the arm.

Hint: It bends in the middle of your arm.

Reverse DRAW to name an area in a hospital.

Hint: Read the word from right to left.

Take the first letters of Bright Owls Observe Keenly. What word appears?

Hint: Read only the capital letters.

A word meaning to observe sounds like a large body of salt water. Give both spellings.

Hint: What do you do with your eyes?

Four printers make four posters in four minutes. At the same individual rate, how long do 20 printers need to make 20 posters?

Hint: How long does one printer take to make one poster?

One word follows rain, sun, and cross to make three familiar compounds. What is it?

Hint: Think of what an archer carries.

Five runners finish in distinct places. Quin is first, Noor is last, Lia is immediately before Mo, and Pax is before Lia. Give the order.

Hint: Place Quin and Noor first, then keep Lia and Mo side by side.

Seven people each shake hands once with every other person. How many handshakes occur?

Hint: Each person shakes 6 hands, but every handshake involves two people.

Starting at 4, alternate multiplying by 2 and subtracting 1. Which term follows 4, 8, 7, 14, 13?

Hint: The last step was subtracting 1, so the next step is the other operation.

Six taps each fill one identical bucket at the same time. If six buckets fill in 12 minutes, how long would one tap take to fill one bucket?

Hint: Each tap fills its own bucket, so the taps do not help one another.

Base, basket, and foot can each take the same ending. Supply it.

Hint: All three are sports.

Ana, Bo, and Cy each have a different pet: cat, dog, or fish. Ana does not have the cat, Bo has the dog, and Cy does not have the fish. Which pet does Ana have?

Hint: Bo's pet is settled. Which pets are left for Ana and Cy?

After a 25 percent discount, a game costs $45. What was its original price?

Hint: $45 is 75 percent of the original price.

A sequence alternates two streams: one counts 2, 4, 6 and the other 10, 20, 30. What comes after 2, 10, 4, 20, 6, 30?

Hint: Read every other term. The next term continues the stream that began with 2.

Take the first of four tablets now and another every 20 minutes. When is the last tablet taken?

Hint: The first tablet is taken now, so count only the gaps between tablets.

Change one letter at a time from COLD to WARM, making a word after every change. Give a four-move route.

Hint: Start by changing the L in COLD.

Three cups contain tea, juice, and water, one drink per cup. Blue has water, red does not have tea, and green does not have juice. What is in red?

Hint: Blue has the water, and green cannot have juice. What does green have?

A price rises by 20 percent and becomes $72. Find the price before the increase.

Hint: $72 is 120 percent of the old price.

The differences in 2, 5, 10, 17, 26 are consecutive odd numbers. Complete the sequence.

Hint: The gaps so far are 3, 5, 7 and 9. What is the next odd number?

Ava says, "Bo is lying." Bo says, "Ava and I are the same type." One always tells the truth and one always lies. Who is who?

Hint: Suppose Ava tells the truth, then check whether Bo's sentence fits.

Find a body organ hidden across the words "the artist."

Hint: Ignore the space and read across both words.

In a reversed-alphabet code, A pairs with Z, B with Y, and so on. Decode WLT.

Hint: W is fourth from the end of the alphabet, so it stands for the fourth letter.

Two whole numbers total 42 and differ by 10. What are they?

Hint: Take 10 off 42 and split what is left in two.

The amount added grows by 3 in 1, 2, 6, 13, 23. What is the next term?

Hint: The amounts added so far are 1, 4, 7 and 10.

Two fathers and two sons share three oranges so that each person receives one. How many people are there?

Hint: One person can be a father and a son at the same time.

All metal widgets are heavy. Widget X is not heavy. What follows?

Hint: If X were a metal widget, what would it have to be?

A square has area 121 square units. What is its perimeter?

Hint: Which number times itself makes 121?

Odd positions count upward by 1 and even positions fall by 10 in 1, 100, 2, 90, 3, 80. Which term is seventh?

Hint: The seventh term is in an odd position, so follow the stream that counts up.

Facing north, turn right, right, left, then around. Which direction are you facing?

Hint: Two right turns face you the opposite way.

All tulips are flowers, and some flowers are yellow. Must some tulips be yellow?

Hint: The yellow flowers might all be daffodils.

Two independent fair coins are tossed. What is the probability of getting exactly one head?

Hint: List the four ways two coins can land.

Two streams are woven together: one adds 3 and the other subtracts 2. Give the next term after 5, 20, 8, 18, 11, 16.

Hint: The next term belongs to the stream that started at 5.

Three closed boxes are labeled APPLES, ORANGES, and MIXED, but every label is wrong. From which box should one fruit be drawn to relabel all three?

Hint: Every label is wrong, so the box labeled MIXED holds only one kind of fruit.

Every club member who swims goes without a hat. Ivo is a club member and wears a hat. Can Ivo be a swimmer under the rule?

Hint: Under the rule, a member who swims never wears a hat.

Name the smallest positive whole number divisible by 4, 6, and 9.

Hint: Try multiples of 9 until one also divides by 4 and by 6.

Forward gaps grow by one letter at a time in B, E, I, N. Which letter is next?

Hint: The gaps are 3, 4 and 5 letters. Move forward 6 from N.

Find the number greater than 40 and less than 50 that is even, divisible by 3, and has digits summing to 6.

Hint: Only one number in the 40s has digits that add up to 6.

Which is the largest three-digit multiple of 7?

Hint: Divide 999 by 7 and look at the remainder.

Backward gaps grow by one letter at a time in Z, W, S, N. Where do you land next?

Hint: Count back from N by one more letter than last time.

A two-digit number has a tens digit one greater than its ones digit, and its digits total 9. What is the number?

Hint: Find two neighboring digits that add up to 9.

Find the sum of the whole numbers from 1 through 20.

Hint: Pair 1 with 20, 2 with 19, and so on.

Triangular numbers begin 1, 3, 6, 10, 15. Continue the pattern once.

Hint: Each step adds one more than the step before: 2, 3, 4, 5.

Tasks W, X, Y, and Z must be done once each. W is before X, Y is after X, and Z is before W. Give the only order.

Hint: Z comes before W, and W before X. Where can Y go?

A positive whole number below 20 leaves remainder 2 when divided by 3 and remainder 4 when divided by 5. Find it.

Hint: List the numbers below 20 that leave 4 when divided by 5.

Successive products form 1, 2, 6, 24, 120 by multiplying by 2, 3, 4, then 5. Extend the pattern.

Hint: The next multiplier is 6.

Talks J, K, L, and M fill slots 1 through 4. M is third, K is after M, L is before J, and L is not second. Give the order.

Hint: M is third and K comes after M, so K takes slot 4.

Five quiz scores have mean 18. If the score 14 is removed, what is the mean of the other four?

Hint: The five scores add up to 90.

Terms follow n times the next whole number: 2, 6, 12, 20, 30 for n from 1 through 5. Find the term for n = 6.

Hint: Check the rule on the last term you have: 5 times 6 is 30.

Exactly two of lamps A, B, C, and D are on. A and B have opposite states, C and D have opposite states, A matches C, and D is on. Which lamps are on?

Hint: D is on, so C is off, and A matches C.

Traveling at a constant 18 kilometers per hour, how far does a cyclist go in 50 minutes?

Hint: 50 minutes is five sixths of an hour.

Beginning at 12, add the digits of the current term to make the next: 12, 15, 21, 24, 30. Continue once.

Hint: The digits of 30 add up to 3.

A bag contains 3 red and 2 blue counters. Two are drawn without replacement. What is the probability both are red?

Hint: After one red counter is drawn, how many reds are left, out of how many counters?

Pair each counting number with twice itself: 1, 2, 2, 4, 3, 6, 4, 8. Which term is ninth?

Hint: The terms come in pairs, and the ninth term starts a new pair.

In a group, 18 people drink tea, 13 drink coffee, and 7 drink both. How many drink at least one of the two?

Hint: The 7 who drink both were counted twice.

Nine coins begin tails-up. One move flips exactly two coins. Can repeated moves leave all nine heads-up?

Hint: Each move changes the number of heads by 0 or by 2. Is 9 even or odd?

Build a five-move word ladder from HEAD to TAIL, changing one letter per move.

Hint: Change the D of HEAD first, to make a word meaning to get better.

A three-digit code obeys these exact clues: 682 has one digit correct and well placed; 614 has one correct but misplaced; 206 has two correct but misplaced; 738 has none correct; 780 has one correct but misplaced. Find the code.

Hint: 738 rules out 7, 3 and 8. Then 780 tells you 0 is in the code, but not last.

Pages are numbered from 1 through 120. How many times is the digit 1 printed?

Hint: Count the 1s in the ones place, the tens place and the hundreds place separately.

Describe each term aloud to obtain the next: 1, 11, 21, 1211, 111221. What follows?

Hint: Read 111221 aloud in groups: three 1s, two 2s, one 1.

Remove two opposite corner squares from an 8 by 8 checkerboard. Can 31 dominoes, each covering two edge-sharing squares, cover what remains?

Hint: Think about the colors. Which color are the two corners you removed?

Exactly one of three suspects took a key, and exactly one statement is true. Ana says, "I did not take it." Bo says, "Ana took it." Cy says, "Bo did not take it." Who took the key?

Hint: Ana's and Bo's statements cannot both be false, so one of them is the true one.

A rectangle has positive whole-number side lengths and area 36. Which side lengths give the smallest perimeter?

Hint: The closer the two sides are to each other, the shorter the way around.

Box 1 says, "The prize is here." Box 2 says, "The prize is not here." Exactly one label is said to be true. Can either box hold the prize without breaking that rule?

Hint: Put the prize in box 1, then in box 2, and count the true labels each time.

A rectangle has positive whole-number side lengths and perimeter 22. Which dimensions give the greatest area?

Hint: Length plus width is 11. Keep the two sides as close as you can.

Nine identical-looking coins include one heavier coin. How can a balance scale identify it in two weighings?

Hint: Split the coins into three groups of three.

Four people take 1, 2, 7, and 10 minutes to cross a bridge. At most two cross, they need one torch, and a pair moves at the slower person's speed. What is the least total time?

Hint: Send the two slowest people across together, and let the two fastest carry the torch back.

Three switches control one indicator in another room. The indicator stays warm for five minutes after it is switched off. You may enter the room once. How can you identify the controlling switch?

Hint: The indicator can tell you more than on or off. Touch it.

Two unevenly burning ropes each take exactly 60 minutes to burn from one end to the other. How can they measure 45 minutes?

Hint: A rope lit at both ends burns out in half the time.

Using only an unmarked 3-liter jug and an unmarked 5-liter jug, measure exactly 4 liters.

Hint: Fill the 5-liter jug and pour it into the 3-liter jug. What is left?

Eight numbered vials include exactly one contaminant that darkens a test strip. How can three strips identify the vial in one test round?

Hint: Three strips that each turn dark or stay clear give 2 times 2 times 2 patterns.

A traveler must ferry a fox, a hen, and grain across a river, carrying only one of them at a time. The fox cannot stay with the hen, and the hen cannot stay with the grain. Give a safe crossing plan.

Hint: The hen causes all the trouble. It goes first, and it may have to come back.

One hundred closed lockers are toggled on pass 1, every second locker on pass 2, every third on pass 3, and so on through pass 100. Which lockers remain open?

Hint: A locker is toggled once for each number that divides it. Which numbers have an odd count of divisors?