115 brain teasers with answers

Name the rule and check that it fits every transition before giving the next term.

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

   23. Add 4 each time.

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

   22. Subtract 5 each time.

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

   243. Multiply by 3 each time.

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

   10. Divide by 2 each time.

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

   26. The operations alternate between multiplying by 2 and subtracting 1.

6. 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?

   8. The odd-position terms are 2, 4, 6, 8 while the even-position terms are 10, 20, 30.

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

   37. Add consecutive odd numbers 3, 5, 7, 9, then 11.

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

   36. The additions are 1, 4, 7, 10, then 13.

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

   4. The odd positions count upward while the even positions fall by 10.

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

    14. One stream adds 3 while the other subtracts 2.

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

    21.

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

    T. The forward gaps are 3, 4, 5, then 6 letters.

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

    H. Move back 3, then 4, then 5, then 6 letters.

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

    February.

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

    36.

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

    21.

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

    13.

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

    720.

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

    312211.

20. 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.

    42.

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

    33.

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

    125.

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

    5.

State assumptions, draw a small model when useful, and explain why alternatives fail.

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

   Four minutes.

2. 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?

   12 minutes.

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

   60 minutes from now.

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

   12:20 p.m.

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

   No.

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

   No. Opposite corners have the same color, while every domino covers one square of each color.

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

   Five socks.

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

   At least two people recorded the same month.

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

   No.

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

    Those poets wear helmets.

11. 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?

    Ava tells the truth and Bo lies.

12. 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?

    No.

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

    Weigh three against three. Keep the heavier group, or the unweighed group if they balance. Then weigh two coins from that group against each other.

14. 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?

    17 minutes.

15. 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?

    Turn on switch 1 for several minutes, turn it off, turn on switch 2, then enter. Lit means switch 2, warm but unlit means switch 1, and cool and unlit means switch 3.

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

    Second place.

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

    Three: a grandfather, his son, and his grandson.

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

    The match.

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

    West.

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

    Light the first rope at both ends and the second rope at one end. When the first is gone, light the other end of the second.

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

    Leave 2 liters in the 5-liter jug, transfer them to the empty 3-liter jug, then fill the 5-liter jug and pour 1 liter into the smaller jug.

22. 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?

    Draw from the box labeled MIXED.

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

    Number the vials 0 through 7 in three-bit binary and put a drop on each strip corresponding to a 1 in the vial's code.

24. 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.

    Take the hen across, return alone, take the fox across, bring the hen back, take the grain across, return alone, then take the hen across.

25. 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?

    The ten lockers numbered by perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Use standard dictionary spellings and show every letter change in the answer.

1. Rearrange LISTEN into a word associated with quiet.

   SILENT.

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

   HEART.

3. Turn COLD into a precious metal by changing one letter.

   GOLD.

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

   HOUSE.

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

   LANE.

6. From TRAIN remove one letter to get precipitation.

   RAIN.

7. Insert one letter into PLAN to make a flying vehicle.

   PLANE.

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

   Add T to make START.

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

   BOW: rainbow, sunbow, and crossbow.

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

    BALL: baseball, basketball, and football.

11. Tooth, hair, and paint share which following word?

    BRUSH: toothbrush, hairbrush, and paintbrush.

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

    COLD, CORD, CARD, WARD, WARM.

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

    HEAD, HEAL, TEAL, TELL, TALL, TAIL.

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

    HEART.

15. An animal is hidden in eduCATION. Which one?

    CAT.

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

    HEAT.

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

    MAP.

18. Rearrange BELOW to name a joint in the arm.

    ELBOW.

19. Reverse DRAW to name an area in a hospital.

    WARD.

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

    BOOK.

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

    SEE and SEA.

Show the equation, count, or case list that makes the numerical answer checkable.

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

   21 handshakes.

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

   24 outfits.

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

   $60.

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

   $60.

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

   600 grams.

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

   32 kilometers.

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

   9.

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

   26 and 16.

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

   7 units.

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

    63 square units.

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

    44 units.

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

    1/5.

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

    1/2.

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

    36.

15. Which is the largest three-digit multiple of 7?

    994.

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

    53 times.

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

    210.

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

    6 by 6, with perimeter 24.

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

    14.

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

    19.

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

    15 kilometers.

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

    3/10.

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

    24 people.

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

    5 by 6, with area 30.

Record the clues first, then give the conclusion and the chain that forces it.

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

   Uma.

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

   Dena, Farah, Eli.

3. 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?

   Third from the left.

4. 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.

   Quin, Pax, Lia, Mo, Noor.

5. 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?

   The fish.

6. 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?

   Juice.

7. 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?

   2 o'clock.

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

   CAT.

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

   DOG.

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

    Box A.

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

    Widget X is not a metal widget.

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

    No.

13. 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?

    No.

14. 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?

    632.

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

    42.

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

    54.

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

    Tuesday.

18. 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.

    Z, W, X, Y.

19. 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.

    L, J, M, K.

20. 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.

    042.

21. 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?

    B and D.

22. 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?

    Bo.