68 brain teasers for adults with answers

Medium and hard reasoning challenges for adult groups, with a checked answer and a short account of the work each puzzle requires.

Updated 27 Sep 2026 · 68 teasers

68 puzzles · 68 brain teasers for adults with answers · answers included

Showing 68 of 68

Medium challenges

Expect a plausible trap or several linked steps.

Starting at 4, alternate multiplying by 2 and subtracting 1. Which term follows 4, 8, 7, 14, 13?
Answer
26. The operations alternate between multiplying by 2 and subtracting 1.
The solver must test and retain two alternating operations.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
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?
Answer
8. The odd-position terms are 2, 4, 6, 8 while the even-position terms are 10, 20, 30.
Two interleaved progressions must be separated and tracked.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
The differences in 2, 5, 10, 17, 26 are consecutive odd numbers. Complete the sequence.
Answer
37. Add consecutive odd numbers 3, 5, 7, 9, then 11.
The first differences must be calculated before their pattern appears.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
The amount added grows by 3 in 1, 2, 6, 13, 23. What is the next term?
Answer
36. The additions are 1, 4, 7, 10, then 13.
The solver needs a difference list and a second pattern within it.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Odd positions count upward by 1 and even positions fall by 10 in 1, 100, 2, 90, 3, 80. Which term is seventh?
Answer
4. The odd positions count upward while the even positions fall by 10.
The prompt signals two tracks, but both must still be checked.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Two streams are woven together: one adds 3 and the other subtracts 2. Give the next term after 5, 20, 8, 18, 11, 16.
Answer
14. One stream adds 3 while the other subtracts 2.
The two position-based rules require modest bookkeeping.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Forward gaps grow by one letter at a time in B, E, I, N. Which letter is next?
Answer
T. The forward gaps are 3, 4, 5, then 6 letters.
Letter positions and changing differences must both be tracked.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Backward gaps grow by one letter at a time in Z, W, S, N. Where do you land next?
Answer
H. Move back 3, then 4, then 5, then 6 letters.
The solver must translate letters to ordered positions and extend the gap pattern.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Triangular numbers begin 1, 3, 6, 10, 15. Continue the pattern once.
Answer
21.
The changing additions must be identified before the next term can be calculated.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Successive products form 1, 2, 6, 24, 120 by multiplying by 2, 3, 4, then 5. Extend the pattern.
Answer
720.
The multiplier changes at every step and must be advanced correctly.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
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.
Answer
42.
The stated formula must be matched to the examples and evaluated once.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Beginning at 12, add the digits of the current term to make the next: 12, 15, 21, 24, 30. Continue once.
Answer
33.
The amount added depends on each changing term rather than on a fixed difference.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Pair each counting number with twice itself: 1, 2, 2, 4, 3, 6, 4, 8. Which term is ninth?
Answer
5.
The sequence must be regrouped into ordered pairs before it can be extended.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Four printers make four posters in four minutes. At the same individual rate, how long do 20 printers need to make 20 posters?
Answer
Four minutes.
A plausible multiplication trap must be rejected by finding the per-printer rate.
Source: OpenStax, Prealgebra 2e, Proportions https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications
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?
Answer
12 minutes.
The solver must distinguish parallel work from sequential work.
Source: OpenStax, Prealgebra 2e, Proportions https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications
Take the first of four tablets now and another every 20 minutes. When is the last tablet taken?
Answer
60 minutes from now.
The first event occurs at time zero, which creates a common off-by-one trap.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
Ava tells the truth and Bo lies.
Both possible assignments must be tested for consistency.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
Two fathers and two sons share three oranges so that each person receives one. How many people are there?
Answer
Three: a grandfather, his son, and his grandson.
Overlapping family roles must replace the default assumption of four people.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Facing north, turn right, right, left, then around. Which direction are you facing?
Answer
West.
Four orientation updates must be tracked without losing the current direction.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
Draw from the box labeled MIXED.
The all-wrong condition must be used to turn one observation into three forced labels.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
One word follows rain, sun, and cross to make three familiar compounds. What is it?
Answer
BOW: rainbow, sunbow, and crossbow.
Three separate compounds must accept the same word.
Source: Merriam-Webster.com Dictionary, "rainbow" https://www.merriam-webster.com/dictionary/rainbow
Base, basket, and foot can each take the same ending. Supply it.
Answer
BALL: baseball, basketball, and football.
Three separate starting words must be tested against one shared ending.
Source: Merriam-Webster.com Dictionary, "baseball" https://www.merriam-webster.com/dictionary/baseball
Change one letter at a time from COLD to WARM, making a word after every change. Give a four-move route.
Answer
COLD, CORD, CARD, WARD, WARM.
Four linked substitutions must keep every intermediate state valid.
Source: Merriam-Webster.com Dictionary, "cold" https://www.merriam-webster.com/dictionary/cold
Find a body organ hidden across the words "the artist."
Answer
HEART.
The answer crosses a word boundary and is not signaled by spacing.
Source: Merriam-Webster.com Dictionary, "heart" https://www.merriam-webster.com/dictionary/heart
Seven people each shake hands once with every other person. How many handshakes occur?
Answer
21 handshakes.
Pairs must be counted without double-counting.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
After a 25 percent discount, a game costs $45. What was its original price?
Answer
$60.
The solver must treat $45 as 75 percent rather than subtracting 25 percent again.
Source: OpenStax, Prealgebra 2e, Proportions https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications
A price rises by 20 percent and becomes $72. Find the price before the increase.
Answer
$60.
The final amount must be recognized as 120 percent of the original.
Source: OpenStax, Prealgebra 2e, Proportions https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications
Two whole numbers total 42 and differ by 10. What are they?
Answer
26 and 16.
Two conditions must be represented and solved together.
Source: OpenStax, Prealgebra 2e, Solving Equations https://openstax.org/books/prealgebra-2e/pages/8-1-solve-equations-using-the-subtraction-and-addition-properties-of-equality
A square has area 121 square units. What is its perimeter?
Answer
44 units.
The side length must first be recovered before the perimeter is found.
Source: OpenStax, Prealgebra 2e, Rectangles, Triangles, and Trapezoids https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids
Two independent fair coins are tossed. What is the probability of getting exactly one head?
Answer
1/2.
All equally likely paired outcomes must be listed without omission.
Source: OpenStax, Prealgebra 2e, Averages and Probability https://openstax.org/books/prealgebra-2e/pages/5-5-averages-and-probability
Name the smallest positive whole number divisible by 4, 6, and 9.
Answer
36.
Three factor requirements must be combined into one least common multiple.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
Which is the largest three-digit multiple of 7?
Answer
994.
A boundary value must be divided, rounded down, and checked.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
Find the sum of the whole numbers from 1 through 20.
Answer
210.
The solver must recognize or construct paired terms rather than add blindly.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
A positive whole number below 20 leaves remainder 2 when divided by 3 and remainder 4 when divided by 5. Find it.
Answer
14.
Two remainder conditions must be intersected over a bounded set.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Five quiz scores have mean 18. If the score 14 is removed, what is the mean of the other four?
Answer
19.
The original total must be reconstructed before a new mean can be calculated.
Source: OpenStax, Prealgebra 2e, Averages and Probability https://openstax.org/books/prealgebra-2e/pages/5-5-averages-and-probability
Traveling at a constant 18 kilometers per hour, how far does a cyclist go in 50 minutes?
Answer
15 kilometers.
Minutes must be converted to a fraction of an hour before applying the rate.
Source: OpenStax, Prealgebra 2e, Proportions https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications
A bag contains 3 red and 2 blue counters. Two are drawn without replacement. What is the probability both are red?
Answer
3/10.
The second probability must use the reduced counts after the first draw.
Source: OpenStax, Prealgebra 2e, Averages and Probability https://openstax.org/books/prealgebra-2e/pages/5-5-averages-and-probability
In a group, 18 people drink tea, 13 drink coffee, and 7 drink both. How many drink at least one of the two?
Answer
24 people.
The overlap must be removed once after it is counted in both totals.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
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.
Answer
Quin, Pax, Lia, Mo, Noor.
A linked two-person block and two fixed endpoints force several placements.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
The fish.
Two eliminations across three one-to-one assignments are required.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
Juice.
The fixed assignment must be removed before two negative clues resolve the rest.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
In a reversed-alphabet code, A pairs with Z, B with Y, and so on. Decode WLT.
Answer
DOG.
Three non-adjacent mirror positions must be translated accurately.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
All metal widgets are heavy. Widget X is not heavy. What follows?
Answer
Widget X is not a metal widget.
The solver must use the contrapositive of a universal rule.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
All tulips are flowers, and some flowers are yellow. Must some tulips be yellow?
Answer
No.
A tempting overlap is not guaranteed by the two set statements.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
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?
Answer
No.
The stated observation must be combined with a universal conditional.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
Find the number greater than 40 and less than 50 that is even, divisible by 3, and has digits summing to 6.
Answer
42.
Several filters must be intersected over a small candidate set.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
A two-digit number has a tens digit one greater than its ones digit, and its digits total 9. What is the number?
Answer
54.
Two digit constraints must be solved together.
Source: OpenStax, Prealgebra 2e, Solving Equations https://openstax.org/books/prealgebra-2e/pages/8-1-solve-equations-using-the-subtraction-and-addition-properties-of-equality
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.
Answer
Z, W, X, Y.
Three precedence clues must be joined into one four-step chain.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
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.
Answer
L, J, M, K.
Fixed placement, relative order, and exclusion clues must be combined.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
B and D.
Four linked binary constraints must be propagated without switching their direction.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html

Hard challenges

Allow working time and ask the solver to explain the route.

Describe each term aloud to obtain the next: 1, 11, 21, 1211, 111221. What follows?
Answer
312211.
The non-arithmetic rule must be inferred and applied to three separate runs of digits.
Source: OpenStax, College Algebra 2e, Sequences https://openstax.org/books/college-algebra-2e/pages/9-1-sequences-and-their-notations
Nine coins begin tails-up. One move flips exactly two coins. Can repeated moves leave all nine heads-up?
Answer
No.
The decisive parity invariant is not obvious from trying individual moves.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Remove two opposite corner squares from an 8 by 8 checkerboard. Can 31 dominoes, each covering two edge-sharing squares, cover what remains?
Answer
No. Opposite corners have the same color, while every domino covers one square of each color.
A non-obvious color invariant proves impossibility without exhaustive placement.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
No.
The solver must exhaust both placements and notice that each makes the labels agree.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html
Nine identical-looking coins include one heavier coin. How can a balance scale identify it in two weighings?
Answer
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.
A three-way outcome must be preserved at each of two planned tests.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
17 minutes.
Several linked crossings must be optimized and lower-cost alternatives compared.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
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 solution must encode three states using both current and stored information.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Two unevenly burning ropes each take exactly 60 minutes to burn from one end to the other. How can they measure 45 minutes?
Answer
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.
The method must avoid assuming that either rope burns at a uniform rate.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Using only an unmarked 3-liter jug and an unmarked 5-liter jug, measure exactly 4 liters.
Answer
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.
Several fills, pours, and empties must preserve an intermediate quantity.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
Eight numbered vials include exactly one contaminant that darkens a test strip. How can three strips identify the vial in one test round?
Answer
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.
Eight possibilities must be encoded into the eight outcome patterns of three binary tests.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
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.
Answer
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.
The plan requires two deliberate returns while maintaining both safety constraints after every trip.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
The ten lockers numbered by perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
A hidden divisor-count invariant replaces an impractical simulation of all passes.
Source: OpenStax, College Algebra, Counting Principles https://openstax.org/books/college-algebra/pages/9-5-counting-principles
Build a five-move word ladder from HEAD to TAIL, changing one letter per move.
Answer
HEAD, HEAL, TEAL, TELL, TALL, TAIL.
Five linked substitutions require planning through valid intermediate words.
Source: Merriam-Webster.com Dictionary, "head" https://www.merriam-webster.com/dictionary/head
Pages are numbered from 1 through 120. How many times is the digit 1 printed?
Answer
53 times.
Overlapping hundreds, tens, and ones cases must be counted systematically.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
A rectangle has positive whole-number side lengths and area 36. Which side lengths give the smallest perimeter?
Answer
6 by 6, with perimeter 24.
All factor pairs must be compared or bounded to prove the minimum.
Source: OpenStax, Prealgebra 2e, Rectangles, Triangles, and Trapezoids https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids
A rectangle has positive whole-number side lengths and perimeter 22. Which dimensions give the greatest area?
Answer
5 by 6, with area 30.
Every whole-number side pair meeting the perimeter constraint must be compared.
Source: OpenStax, Prealgebra 2e, Rectangles, Triangles, and Trapezoids https://openstax.org/books/prealgebra-2e/pages/9-4-use-properties-of-rectangles-triangles-and-trapezoids
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.
Answer
042.
Five exact-count clues must be intersected while tracking both membership and position.
Source: NRICH, Using NRICH Tasks to Develop Key Problem-Solving Skills https://nrich.maths.org/articles/using-nrich-tasks-develop-key-problem-solving-skills
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?
Answer
Bo.
All three culprit cases must be checked against an exact truth count.
Source: Open Logic Project, forall x: Calgary https://forallx.openlogicproject.org/html/Ch11.html

How to play

Read the prompt once, give everyone quiet working time, then ask for the route before revealing the checked answer.

Plan the round and team scores

Seconds per turnTurns in the session

8 turns × 60 seconds = 8 minutes of play, plus instructions and breaks.

Pause whenever the group needs more time.

Teams

Team Lime is acting

Team Lime: 0

Team Violet: 0

Games and printables

Find a game

68 brain teasers for adults with answers