32 brain teasers for teens with answers
Number, pattern, word and deduction puzzles for ages 11 to 18, each marked easy, medium or hard. Every answer shows the reasoning, so a class or group can check the method as well as the result.
Updated
Number puzzles
How can you take one away from nineteen and be left with twenty? Think about how nineteen can be written.
easy
Write nineteen in Roman numerals, XIX, and take away the I. XX is twenty.
In Roman numerals nineteen is X (ten) followed by IX (nine). Removing the I in the middle leaves XX, two tens.
In a number pyramid, each number is the sum of the two numbers just below it. The bottom row reads 3, ?, ?. The middle row reads 10, 13. Find the two missing bottom numbers and the number at the top.
easy
Bottom row 3, 7, 6. Top 23.
3 + 7 = 10, so the second bottom number is 7. Then 7 + 6 = 13, so the third is 6. The top is 10 + 13 = 23.
I am a two-digit number. I am a perfect square and also a perfect cube. What number am I?
easy
64.
The two-digit squares are 16, 25, 36, 49, 64 and 81. The two-digit cubes are 27 and 64. Only 64 is on both lists: it is 8 x 8 and also 4 x 4 x 4.
Today is Wednesday. What day of the week will it be 100 days from today?
easy
Friday.
Every 7 days brings you back to Wednesday. 100 = 14 x 7 + 2, so after 98 days it is Wednesday again, and 2 more days make it Friday.
The digits of a two-digit number add up to 11. Swap the digits and the number grows by 27. What is the number?
medium
47.
Swapping the digits of a two-digit number changes it by 9 times the difference between the digits, so these digits differ by 27 / 9 = 3. Two digits that add to 11 and differ by 3 are 4 and 7. The number grows, so the smaller digit comes first: 74 - 47 = 27.
Use each of the digits 1, 2, 3 and 4 once to make two two-digit numbers. Which two numbers give the largest possible product when multiplied?
medium
41 and 32, which give 1312.
The biggest digits, 4 and 3, belong in the tens places. That leaves 41 x 32 = 1312 or 42 x 31 = 1302. Giving the extra 2 to the smaller tens digit keeps the two numbers closer together, and closer numbers with the same total give a bigger product.
Zoe spends half of her money plus $1 at the first shop. At the second shop she spends half of what is left plus $1, and then she has nothing. How much did she start with?
medium
$6.
Work backward. Before the second shop she had an amount whose half plus $1 is all of it, so half of it is $1 and the amount is $2. Before the first shop, half of her money plus $1 left $2, so half of her money was $3 and she started with $6. Check: 6 - (3 + 1) = 2, and 2 - (1 + 1) = 0.
You can climb a staircase 1 or 2 steps at a time. In how many different ways can you climb 5 steps?
medium
8 ways.
Count upward. There is 1 way to climb 1 step and 2 ways to climb 2 (1 + 1, or 2). Your last move onto any step is either 1 step or 2 steps, so the counts for the two steps below add up: 3 steps have 1 + 2 = 3 ways, 4 steps have 2 + 3 = 5 and 5 steps have 3 + 5 = 8.
Pick a three-digit number whose first digit is at least 2 more than its last digit, such as 732. Subtract its reverse (237). Then add the result to its own reverse. What do you get, and does it depend on the number you picked?
medium
1089, whatever number you pick.
With 732: 732 - 237 = 495, and 495 + 594 = 1089. The subtraction always gives a number with 9 in the middle and outer digits that add to 9, such as 198, 297 or 495. Reversing keeps the 9 in the middle and swaps the outer digits, so the sum is always 900 + 180 + 9 = 1089.
Using 1, 3, 4 and 6 once each, with any of +, -, x and / and as many brackets as you like, make 24.
hard
6 / (1 - 3/4) = 24.
1 - 3/4 = 1/4, and dividing 6 by 1/4 is the same as multiplying it by 4, which gives 24. The obvious 4 x 6 = 24 fails, because the 1 and the 3 cannot be combined into 1 or 0 to leave 24 unchanged. This is the only way to reach 24 with these four numbers.
A chocolate bar is a 4 by 6 grid of 24 small squares. Each snap breaks one piece into two along a straight line, and you may not stack pieces. How many snaps does it take to separate all 24 squares?
medium
23 snaps.
Each snap turns one piece into two, so it adds exactly one piece. You start with 1 piece and need 24, so every method takes 24 - 1 = 23 snaps.
Pattern puzzles
Which number is the odd one out: 13, 17, 19, 21, 23?
easy
21.
13, 17, 19 and 23 are prime numbers: nothing divides them except 1 and themselves. 21 is 3 x 7, so it is not prime.
What comes next: 1:00, 2:05, 3:10, 4:15, ?
easy
5:20.
Each time is 1 hour and 5 minutes later than the one before.
A number machine turns 2 into 5, 3 into 10 and 4 into 17. What does it turn 5 into?
easy
26.
The machine multiplies the number by itself and adds 1: 2 x 2 + 1 = 5, 3 x 3 + 1 = 10 and 4 x 4 + 1 = 17. So 5 becomes 5 x 5 + 1 = 26.
What comes next: 31, 28, 31, 30, 31, 30, ?
medium
31.
These are the numbers of days in January to June of a year that is not a leap year. The next month, July, has 31 days.
1 x 1 = 1, 11 x 11 = 121 and 111 x 111 = 12321. Without a calculator, what is 11111 x 11111?
medium
123454321.
Each answer counts up to the number of 1s and back down: 1111 x 1111 = 1234321, so 11111 x 11111 = 123454321. In the long multiplication, each column adds up as many 1s as line up in it, which is why the digits rise and fall.
What comes next: 1, 4, 27, 256, ?
medium
3125.
Each term is a number multiplied by itself that many times: 1, then 2 x 2 = 4, then 3 x 3 x 3 = 27, then 4 x 4 x 4 x 4 = 256. Next is 5 x 5 x 5 x 5 x 5 = 3125.
What comes next: 61, 52, 63, 94, 46, ?
hard
18.
Reverse each number: 16, 25, 36, 49, 64. These are the squares of 4, 5, 6, 7 and 8. The next square is 9 x 9 = 81, which reversed is 18.
What letter comes next: A, E, F, H, I, K, L, M, N, ?
hard
T.
These are the capital letters drawn only with straight lines. O, P, Q, R and S all have curves, so the next straight-line capital is T.
Word puzzles
Rearrange the letters of NEW DOOR to make one word.
easy
ONE WORD.
NEW DOOR and ONE WORD use the same seven letters, and ONE WORD is exactly what the puzzle asked for.
A country is hidden in this sentence, running across the gap between two words: "Could you pass the pita, Lynn?" Which country?
easy
Italy.
Ignore the comma and the space in "pita, Lynn" and the letters I, T, A, L, Y sit side by side.
Rearrange the letters of DORMITORY into a two-word phrase that could describe a messy one.
medium
DIRTY ROOM.
DORMITORY and DIRTY ROOM use the same nine letters: D, I, M, O, O, R, R, T and Y.
Rearrange the letters of ELEVEN PLUS TWO into another sum with the same answer.
medium
TWELVE PLUS ONE.
Both phrases use the same 13 letters, and both sums come to 13: 11 + 2 = 12 + 1.
Which ten-letter word, the name of an old writing machine, can be typed using only the top row of letters on a standard English keyboard?
medium
TYPEWRITER.
The top letter row of a standard English keyboard is Q, W, E, R, T, Y, U, I, O, P. Every letter of TYPEWRITER (T, Y, P, E, W, R, I) is on that row.
What do these four words have in common: DEFT, FIRST, CANOPY, STUDY?
hard
Each contains three letters that follow one another in the alphabet.
DEFT has D, E, F. FIRST has R, S, T. CANOPY has N, O, P. STUDY has S, T, U.
Deduction puzzles
Ten coins lie on a table. You and a friend take turns removing 1 or 2 coins, and whoever takes the last coin wins. Should you go first, and how can you make sure you win?
medium
Go first and take 1 coin. After that, always take 3 minus whatever your friend just took.
Whoever has to move with 3 coins left loses: whether they take 1 or 2, the other player takes the rest. The same is true with 6 or 9 coins left, because the other player can always bring the total down by 3 per round. Taking 1 of the 10 leaves your friend facing 9, and answering each of their moves so that the round removes 3 leaves them 6, then 3, then none.
Ava, Ben, Cole, Dina and Eli stand in a line. Ben is somewhere behind Dina. Cole is directly behind Ava. Eli is not at either end. Dina is not at the front. Eli is not next to Ben. What is the order from front to back?
medium
Ava, Cole, Eli, Dina, Ben.
The front cannot be Dina (a clue), Eli (not at an end), Ben (he is behind Dina) or Cole (he is behind Ava), so Ava is first and Cole second. Eli is third or fourth. If Eli were fourth, Dina would be third and Ben fifth, next to Eli. So Eli is third, Dina fourth and Ben last.
Six glasses stand in a row. The first three are full of water and the last three are empty. By moving only one glass, make the row alternate: full, empty, full, empty, full, empty. How?
medium
Pick up the second glass, pour its water into the fifth glass, and put it back.
The row starts full, full, full, empty, empty, empty. Pouring glass 2 into glass 5 empties the second glass and fills the fifth, so the row reads full, empty, full, empty, full, empty. Only one glass was moved.
On an ordinary die, opposite faces always add up to 7. You can see the 1, 2 and 3 faces meeting at one corner. What do the three faces you cannot see add up to?
easy
15.
The hidden faces are the ones opposite the faces you can see: 6 is opposite 1, 5 is opposite 2 and 4 is opposite 3. 6 + 5 + 4 = 15, which is also 3 x 7 - (1 + 2 + 3).
You see an analog clock with no numbers on its face in a mirror, and it seems to show 3:40. What time is it really?
medium
8:20.
A mirror flips the clock left to right, so a hand that really points a certain distance to one side of 12 appears the same distance to the other side. The real time and the mirror time add up to 12:00: 3:40 + 8:20 = 12:00. Check the minute hand: at 20 minutes it points to the right of 12, and the mirror shows it on the left at 40 minutes.
You have a 7-minute sand timer and a 4-minute sand timer. How can you time exactly 9 minutes?
hard
Start both. When the 4-minute timer runs out, turn it over. When the 7-minute timer runs out, turn it over. When the 4-minute timer runs out again, turn the 7-minute timer over once more. When it runs out, 9 minutes have passed.
The 4-minute timer runs out at 4 minutes and again at 8. The 7-minute timer runs out at 7 and restarts, so at 8 minutes it has 1 minute of sand in the bottom. Turning it over sends that 1 minute back to the top, and it runs out at 9 minutes.
Twenty coins lie on a table: 10 heads up and 10 tails up. You are blindfolded and cannot feel which side is up, but you may move and flip coins. How can you split them into two piles with the same number of heads?
hard
Take any 10 coins as one pile and flip every coin in it.
Say your pile of 10 holds h heads. The other pile then holds the remaining 10 - h heads. Your pile has 10 - h tails, so after you flip all of it, it has 10 - h heads, the same as the other pile.
Plan the round and team scores
8 turns × 60 seconds = 8 minutes of play, plus instructions and breaks.
60
These are adjustable house rules. Pause whenever the group needs more time.
Team 1: 0
Team 2: 0
Use this set with a group
Read a prompt, allow thinking time, then invite an answer or a pass. For a timed round, choose a turn length before starting. A host can keep the printed answers out of view until the round ends.