115 brain teasers with answers

23. Add 4 each time.

The consecutive differences are 4, 4, and 4, so 19 + 4 = 23.

22. Subtract 5 each time.

Each term is 5 less than the previous term, so 27 - 5 = 22.

243. Multiply by 3 each time.

Each term divided by the previous term is 3, so 81 x 3 = 243.

10. Divide by 2 each time.

Each term is half the previous term, and half of 20 is 10.

21.

The previous two terms are 8 and 13, and 8 + 13 = 21.

February.

Three months after November is February of the next year.

36.

The terms are 1 squared, 2 squared, 3 squared, 4 squared, and 5 squared. The sixth term is 6 squared, which is 36.

13.

The integer after 11 is 12, which has factors other than 1 and itself. The next integer, 13, has only 1 and 13 as positive factors.

125.

The terms are 1 cubed through 4 cubed. The next is 5 cubed = 5 x 5 x 5 = 125.

12:20 p.m.

9:35 plus 2 hours is 11:35, and another 45 minutes is 12:20.

Five socks.

The first four socks could all differ. A fifth must match one of those four colors.

At least two people recorded the same month.

Twelve labels cannot hold 13 records with at most one record per label.

No.

Amber implies round, and round excludes wooden, so amber excludes wooden.

Those poets wear helmets.

Every member of the cyclist set wears a helmet, including the poets in that set.

Second place.

Passing the second-place runner puts you in that runner's former position.

The match.

The match must be burning before it can light any listed object.

SILENT.

LISTEN and SILENT each contain E, I, L, N, S, and T exactly once.

HEART.

EARTH and HEART use the same letters: A, E, H, R, and T.

GOLD.

Replacing C with G changes COLD to GOLD.

HOUSE.

Replacing M with H changes MOUSE to HOUSE.

LANE.

PLANE without its first letter P is LANE.

RAIN.

Removing T from TRAIN leaves RAIN.

PLANE.

Adding E after PLAN produces PLANE.

Add T to make START.

Appending T to STAR spells START.

BRUSH: toothbrush, hairbrush, and paintbrush.

Appending BRUSH forms TOOTHBRUSH, HAIRBRUSH, and PAINTBRUSH.

CAT.

eduCATION contains C, A, T consecutively.

HEAT.

Alphabet positions 8, 5, 1, and 20 are H, E, A, and T.

MAP.

Alphabet positions 13, 1, and 16 are M, A, and P.

ELBOW.

BELOW and ELBOW each contain B, E, L, O, and W exactly once.

WARD.

Reading the letters D-R-A-W from right to left gives W-A-R-D.

BOOK.

The initial letters of Bright, Owls, Observe, and Keenly are B, O, O, and K.

SEE and SEA.

SEE means to perceive or observe, while SEA names a large body of salt water; both are pronounced the same way.

24 outfits.

The multiplication principle gives 3 x 4 x 2 = 24.

600 grams.

240 / 6 = 40 grams per muffin, and 40 x 15 = 600 grams.

32 kilometers.

12 / 3 = 4 kilometers per centimeter, and 8 x 4 = 32 kilometers.

9.

3x + 4 = 31, so 3x = 27 and x = 9.

7 units.

2 x (12 + width) = 38, so 12 + width = 19 and the width is 7.

63 square units.

Triangle area is one-half x base x height, so 14 x 9 / 2 = 63.

1/5.

There are 2 green counters among 10 total, and 2/10 simplifies to 1/5.

Uma.

The clues form the order Uma, Rae, Sol, Tia.

Dena, Farah, Eli.

Dena is above both others, and Farah is explicitly above Eli.

Third from the left.

P occupies 1, Q occupies 2, and S occupies 4, leaving position 3 for R.

2 o'clock.

With science at 3, art and music occupy 1 and 2. Art must be earlier, so music is at 2.

CAT.

Moving D, B, and U back one letter gives C, A, and T.

Box A.

Opening B requires A's key, and opening C requires B's key, so A must precede both.

632.

Twice 3 is 6, and one less than 3 is 2.

Tuesday.

The days after Monday and before Thursday are Tuesday and Wednesday; excluding Wednesday leaves Tuesday.

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

4 x 2 = 8, 8 - 1 = 7, 7 x 2 = 14, 14 - 1 = 13, then 13 x 2 = 26.

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

Positions 1, 3, and 5 rise by 2, so position 7 is 8.

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

The differences are 3, 5, 7, and 9; the next difference is 11, and 26 + 11 = 37.

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

The differences increase by 3: 1, 4, 7, 10, 13. Therefore 23 + 13 = 36.

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

Odd positions 1, 3, 5, and 7 contain 1, 2, 3, and 4.

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

Odd positions are 5, 8, 11, so the next odd-position term is 14.

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

B to E is 3, E to I is 4, I to N is 5, and six letters after N is T.

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

N is the 14th letter; moving back 6 positions reaches the 8th letter, H.

21.

The additions are 2, 3, 4, and 5. Adding the next amount, 6, to 15 gives 21.

720.

The next multiplier is 6, so the next term is 120 x 6 = 720.

42.

For n = 6, the rule gives 6 x (6 + 1) = 6 x 7 = 42.

33.

The shown steps add 1 + 2, then 1 + 5, then 2 + 1, then 2 + 4. The digits of 30 total 3, so 30 + 3 = 33.

5.

The pairs are (1, 2), (2, 4), (3, 6), and (4, 8). The next pair begins with 5, so the ninth term is 5.

Four minutes.

Each printer makes one poster in four minutes, so 20 printers make 20 posters in four minutes.

12 minutes.

Each tap is paired with one bucket, so the individual fill time is the observed 12 minutes.

60 minutes from now.

The four tablet times are 0, 20, 40, and 60 minutes.

Ava tells the truth and Bo lies.

If Ava is truthful, Bo lies and his same-type claim is false. Reversing the roles makes Bo's same-type claim false even though he would be truthful.

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

The middle person is both a father and a son, satisfying all four role descriptions among three people.

West.

North becomes east, south, east, then west after the half-turn.

Draw from the box labeled MIXED.

The box labeled MIXED cannot be mixed. If the drawn fruit is an apple, that box is APPLES; the box labeled ORANGES cannot be oranges and cannot now be apples, so it is MIXED, leaving ORANGES for the last box. If the draw is an orange, the same reasoning works with the fruit names exchanged.

BOW: rainbow, sunbow, and crossbow.

Appending BOW forms RAINBOW, SUNBOW, and CROSSBOW.

BALL: baseball, basketball, and football.

Appending BALL forms BASEBALL, BASKETBALL, and FOOTBALL.

COLD, CORD, CARD, WARD, WARM.

Each adjacent pair differs in exactly one position, and every listed form is a word.

HEART.

tHE ARTist contains the consecutive letters H, E, A, R, T.

21 handshakes.

There are 7 x 6 ordered choices, and dividing by 2 gives 21 unordered pairs.

$60.

0.75 times the original price equals 45, so the original price is 45 / 0.75 = 60.

$60.

1.2 times the original price equals 72, and 72 / 1.2 = 60.

26 and 16.

x + y = 42 and x - y = 10. Adding gives 2x = 52, so x = 26 and y = 16.

44 units.

The positive square root of 121 is 11, and 4 x 11 = 44.

1/2.

The outcomes are HH, HT, TH, and TT. Two of four have exactly one head, so the probability is 2/4 = 1/2.

36.

The required prime factors are 2 squared and 3 squared, whose product is 36.

994.

999 / 7 is 142 remainder 5, so the largest whole multiplier is 142 and 142 x 7 = 994.

210.

Pair 1 with 20, 2 with 19, and so on. Ten pairs each total 21, giving 210.

14.

The numbers below 20 that leave remainder 4 upon division by 5 are 4, 9, 14, and 19. Their remainders upon division by 3 are 1, 0, 2, and 1, so only 14 satisfies both conditions.

19.

A mean of 18 across five scores gives a total of 5 x 18 = 90. Removing 14 leaves 76, and 76 / 4 = 19.

15 kilometers.

Fifty minutes is 50/60 = 5/6 of an hour. Distance equals rate times time, so 18 x 5/6 = 15 kilometers.

3/10.

The first red has probability 3/5. After it is removed, the second red has probability 2/4. Multiplying gives 3/5 x 2/4 = 6/20 = 3/10.

24 people.

Adding 18 and 13 counts the 7 people in both groups twice. Subtracting that duplicate count gives 18 + 13 - 7 = 24.

Quin, Pax, Lia, Mo, Noor.

Positions 1 and 5 are fixed. Lia-Mo cannot use 2-3 because Pax must be before Lia, so Pax, Lia, and Mo fill 2, 3, and 4.

The fish.

Bo uses dog. Cat and fish remain; Cy cannot take fish, so Cy has cat and Ana has fish.

Juice.

Blue uses water. Tea and juice remain; green cannot use juice, so green has tea and red has juice.

DOG.

W mirrors D, L mirrors O, and T mirrors G.

Widget X is not a metal widget.

If X were a metal widget, the premise would make it heavy, contradicting the stated fact.

No.

The yellow flowers could all be non-tulips, so the premises allow a case with no yellow tulips.

No.

Swimming would imply no hat, which conflicts with Ivo wearing a hat.

42.

The multiples of 3 in the range are 42, 45, and 48. Only 42 is even and has digit sum 6.

54.

If the ones digit is x, the tens digit is x + 1. Then 2x + 1 = 9, so x = 4 and the number is 54.

Z, W, X, Y.

Z precedes W, W precedes X, and X precedes Y, so the full order is forced.

L, J, M, K.

M occupies slot 3, so K must be slot 4. Slots 1 and 2 remain for L and J; because L is before J and is not second, L is slot 1 and J is slot 2.

B and D.

D is on, so its opposite C is off. A matches C, so A is off. B is opposite A, so B is on. Therefore exactly B and D are on, satisfying the stated total of two.

312211.

The last shown term has three 1s, two 2s, and one 1. Writing those counts and digits in order gives 31 22 11, or 312211.

No.

The number of heads changes by 2, 0, or -2, so it always stays even. Nine heads is odd.

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

The board starts with 32 squares of each color. Removing same-colored corners leaves 30 of one color and 32 of the other, but 31 dominoes would cover 31 of each.

No.

With the prize in box 1, both labels are true. With it in box 2, both labels are false.

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.

The first weighing narrows nine candidates to three. The second distinguishes left, right, or the unweighed third coin.

17 minutes.

Crossing the two slowest together costs at least 10. The two fastest can enable that crossing and restore the torch for 2 + 1 + 10 + 2 = 15, after which their final crossing costs 2. Sending the slowest separately costs at least 21, so 17 is minimal.

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.

The procedure deliberately creates three distinguishable states: on, recently off, and never on.

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.

Burning the first rope from both ends consumes it in 30 minutes even if its rate varies along its length. The second rope then has 30 minutes of one-end burn time left; lighting its other end halves that remaining time to 15 minutes. The total is 30 + 15 = 45 minutes.

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.

Fill the 5-liter jug and pour into the 3-liter jug, leaving 2 liters. Empty the smaller jug and move those 2 liters into it. Refill the 5-liter jug; the smaller jug needs 1 more liter, so filling it leaves exactly 4 liters in the larger jug.

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.

Three strips have 2 x 2 x 2 = 8 light-or-dark patterns. Treating dark as 1 and unchanged as 0 makes the observed three-bit pattern equal the contaminated vial's number; 000 identifies vial 0.

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.

After the first trip, the fox and grain are safe together. Swapping the fox for the hen leaves the fox with grain across the river. Moving the grain next leaves the hen alone, and the final trip reunites all three without ever leaving a forbidden pair unattended.

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

Locker n is toggled once for each positive divisor of n. Divisors normally pair as d and n/d, giving an even number of toggles. Only perfect squares have one unpaired divisor, their square root, so exactly the square-numbered lockers receive an odd number of toggles and finish open.

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

Each adjacent pair changes exactly one letter: D/L, H/T, A/L, E/A, then L/I.

53 times.

From 1 to 99 there are 20. From 100 to 120 there are 21 hundreds digits, 10 tens digits, and 2 ones digits: 20 + 21 + 10 + 2 = 53.

6 by 6, with perimeter 24.

The factor pairs are 1x36, 2x18, 3x12, 4x9, and 6x6, with perimeters 74, 40, 30, 26, and 24.

5 by 6, with area 30.

The side lengths must total 11. The possible pairs 1x10, 2x9, 3x8, 4x7, and 5x6 have areas 10, 18, 24, 28, and 30, so 5 by 6 is greatest.

042.

From 738, digits 7, 3, and 8 are absent. The 780 clue then makes 0 present but not third. In 682, 2 must be the well-placed third digit or 6 must be first; the 614 misplaced clue rules out a well-placed 6, so 6 is absent and 2 is third. The 206 clue puts 0 and 2 in the code but not in positions 2 and 1, so 0 is first. In 614, 1 cannot occupy its shown second position, leaving 4 as the one correct misplaced digit in the remaining second slot.

Bo.

If Ana took it, Ana's statement is false while Bo's and Cy's are true, giving two truths. If Cy took it, Ana's and Cy's are true, again giving two. If Bo took it, only Ana's statement is true: Bo's accusation is false and Cy's claim is false. Therefore Bo is the sole consistent culprit.