Logic puzzles train exactly the skills that schoolwork needs: reading carefully, testing assumptions, working step by step and checking your answer. They also make excellent bell-ringers, brain breaks and early-finisher tasks.
Here are 30 brain teasers for teens, grouped into five sets that get gradually harder. Answers are hidden under each set. Try each puzzle before you look, and if you get one wrong, work out why the answer is right. That is where the learning happens.
In this guide7 sections
Set 1: Read carefully (1–6)
These look easy, and most people get at least one wrong on the first try. Three of them (4, 5 and 6) come from the Cognitive Reflection Test, which psychologists use to measure whether people stop to check an intuitive answer.
- A farmer has 17 sheep. All but 9 run away. How many sheep are left?
- How many months have 28 days?
- You are running a race and you pass the person in second place. What place are you in now?
- A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
- If 5 machines take 5 minutes to make 5 widgets, how long would 100 machines take to make 100 widgets?
- A patch of lily pads doubles in size every day. It takes 48 days to cover the whole lake. How long does it take to cover half the lake?
Answers to Set 1
- 9. “All but 9” means 9 stayed.
- All 12. Every month has at least 28 days.
- Second. You took second place; the leader is still ahead.
- 5 cents. If the ball is $0.05, the bat is $1.05, and the total is $1.10. The intuitive answer of 10 cents makes the total $1.20.
- 5 minutes. Each machine makes one widget in 5 minutes, so 100 machines make 100 widgets in 5 minutes.
- 47 days. It doubles every day, so the day before it covers the whole lake, it covers half.
Set 2: Number puzzles (7–14)
- I am a two-digit number. My digits add up to 9. If you reverse my digits, the new number is 27 more than me. What number am I?
- What is the smallest number that leaves a remainder of 1 when divided by 2, 3, 4, 5 or 6, but is exactly divisible by 7?
- Three consecutive whole numbers add up to 72. What are they?
- How many squares of all sizes are there on a standard 8×8 chessboard?
- A clock takes 5 seconds to strike 6 o’clock. How long does it take to strike 12 o’clock?
- Ten people meet, and every person shakes hands once with every other person. How many handshakes are there?
- What comes next? 1, 11, 21, 1211, 111221, …
- Using exactly four 4s and any of +, −, × and ÷, make the number 7.
Answers to Set 2
- 36. Reversed it is 63, which is 27 more, and 3 + 6 = 9.
- 301. Numbers that leave remainder 1 for 2, 3, 4, 5 and 6 are one more than a multiple of 60: 61, 121, 181, 241, 301… The first divisible by 7 is 301 = 7 × 43.
- 23, 24 and 25. The middle number is 72 ÷ 3 = 24.
- 204. There are 64 squares of size 1×1, 49 of 2×2, 36 of 3×3 and so on down to 1 of 8×8: 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204.
- 11 seconds. Six strikes have 5 gaps, so each gap is 1 second. Twelve strikes have 11 gaps.
- 45. Each of the 10 people shakes 9 hands, but that counts every handshake twice: 10 × 9 ÷ 2 = 45.
- 312211. Each term describes the previous one: 111221 is “three 1s, two 2s, one 1,” which is 312211. It is called the look-and-say sequence.
- 44 ÷ 4 − 4 = 7, or 4 + 4 − 4 ÷ 4 = 7.
Set 3: Deduction (15–21)
- Three boxes are labeled “Apples,” “Oranges” and “Apples and Oranges.” Every label is wrong. You may take one fruit from one box without looking inside. How can you label all three boxes correctly?
- You face two doors. One leads to freedom, the other does not. Each door has a guard: one always tells the truth and one always lies, but you don’t know which is which. You may ask one guard one question. What do you ask?
- Three switches outside a closed room control one light bulb inside. You can flip the switches as much as you like, but you may enter the room only once. How can you tell which switch controls the bulb?
- On an island, knights always tell the truth and knaves always lie. A says: “We are both knaves.” What are A and B?
- Alice, Ben and Chloe are a pianist, a painter and a chess player, in some order. Alice is not the painter. The chess player is older than Ben. Chloe is the youngest of the three. The painter is not the youngest. Who does what?
- Dev, Emma, Farah and Gus sit in a row of four seats. Farah sits at the left end. Emma is not at either end. Gus sits immediately to the right of Dev. What is the order from left to right?
- On a game show, a prize is behind one of three doors. You pick door 1. The host, who knows where the prize is, opens door 3 to show it is empty, then offers you the chance to switch to door 2. Should you switch?
Answers to Set 3
- Take a fruit from the box labeled “Apples and Oranges.” Its label is wrong, so it contains only one kind. If you pull out an apple, it is the Apples box. The box labeled “Oranges” cannot hold only oranges (its label is wrong) and cannot hold only apples (you found those), so it is the mixed box. The last box is Oranges. The same logic works if you pull out an orange.
- Ask either guard: “If I asked the other guard which door leads to freedom, what would he say?” Then choose the other door. Either way, the answer passes through exactly one lie, so it always points to the wrong door.
- Turn switch 1 on for a few minutes, then turn it off. Turn switch 2 on and go in. If the bulb is on, it is switch 2. If it is off but warm, it is switch 1. If it is off and cold, it is switch 3.
- A is a knave and B is a knight. A knight could never say “we are both knaves,” so A is a knave. A’s statement is therefore false, so they are not both knaves, which means B is a knight.
- Alice is the chess player, Ben is the painter and Chloe is the pianist. The chess player is older than Ben, so Ben is not the chess player; Chloe is the youngest, so she isn’t either. That leaves Alice. The painter is not the youngest, so Chloe is the pianist and Ben the painter.
- Farah, Emma, Dev, Gus. Farah takes seat 1. Emma must be in seat 2 or 3. Dev and Gus need two seats side by side, so they take seats 3 and 4, leaving seat 2 for Emma.
- Yes, switch. Your first pick is right only 1 time in 3. The host always opens an empty door, so switching wins the other 2 times in 3. This is the Monty Hall problem, and it fooled many mathematicians when it was first popularized.
Set 4: Patterns (22–26)
What comes next in each sequence?
- 2, 6, 12, 20, 30, …
- 1, 4, 9, 16, 25, …
- O, T, T, F, F, S, S, E, …
- J, F, M, A, M, J, J, …
- 3, 5, 9, 17, 33, …
Answers to Set 4
- 42. The numbers are 1×2, 2×3, 3×4, 4×5, 5×6, so next is 6×7. (The gaps also grow by 2 each time.)
- 36. Square numbers: 6² = 36.
- N. First letters of One, Two, Three, Four, Five, Six, Seven, Eight, Nine.
- A. First letters of the months: January to July, then August.
- 65. Each term is double the previous one minus 1: 33 × 2 − 1 = 65.
Want more? The Number Patterns games on our site, such as Add the Last Two, give you an endless supply.
Set 5: Classic strategy puzzles (27–30)
- A farmer must take a wolf, a goat and a cabbage across a river. The boat holds the farmer and only one item. Left alone, the wolf will eat the goat and the goat will eat the cabbage. How does the farmer get everything across?
- Four people must cross a narrow bridge at night with one flashlight. At most two can cross at once, and anyone crossing needs the flashlight. They take 1, 2, 5 and 10 minutes to cross; a pair moves at the slower person’s speed. What is the shortest time for everyone to cross?
- You have a 3-liter jug and a 5-liter jug, and plenty of water. How do you measure exactly 4 liters?
- You have 9 identical-looking coins. One is slightly heavier. Using a balance scale only twice, how do you find the heavy coin?
Answers to Set 5
- Take the goat across and come back. Take the wolf across and bring the goat back. Take the cabbage across and come back. Finally take the goat across. The goat is never left alone with the wolf or the cabbage.
- 17 minutes. The 1 and 2 cross (2 min). The 1 returns (1). The 5 and 10 cross together (10). The 2 returns (2). The 1 and 2 cross again (2). Total: 2 + 1 + 10 + 2 + 2 = 17. The key insight is to send the two slowest people together.
- Fill the 5-liter jug and pour into the 3-liter jug until it is full, leaving 2 liters. Empty the 3-liter jug and pour the 2 liters into it. Fill the 5-liter jug again and top up the 3-liter jug (it takes 1 liter). 4 liters remain in the 5-liter jug.
- Split the coins into three groups of three. Weigh two groups. If one side is heavier, the heavy coin is in that group; if they balance, it is in the third group. Then take the three coins from that group and weigh one against another. The heavier one is the coin; if they balance, it is the third coin.
How to use these puzzles in class
- Bell-ringer: put one puzzle on the board as students arrive and discuss it after attendance.
- Brain break: a quick Set 1 or Set 4 puzzle resets attention in two minutes. See more ideas in our two-minute brain breaks.
- Team challenge: give each group a set and award points for correct answers and clear explanations.
- Early finishers: keep a printed set at the front of the room.
- Math connection: puzzles 7–12 are algebra, number theory and combinatorics in disguise. Pair them with our mental math tricks.
For quick logic games on the projector, try Quiz: Logic Puzzles or the Guess the Number game, which secretly teaches binary search.
Frequently asked questions
Are logic puzzles good for teenagers?
Yes. They build careful reading, step-by-step reasoning and the habit of checking your first instinct, which are useful in math, science and everyday decisions.
What is the hardest puzzle on this list?
Most people find the Monty Hall problem (21) and the bridge crossing (28) hardest, because the intuitive answer is wrong.
How can I get better at logic puzzles?
Slow down, write down what you know, test small cases and check your answer against every condition. After each puzzle, explain the solution out loud. Explaining it is what makes the method stick for the next one.
