10 Fun Math Logic Puzzles for Kids (With Answers)
Ten original logic and number puzzles for grades 3 to 6, each tied to a skill math contests reward, with worked answers at the end and a free daily game to keep practicing.
· 8 min read
Prep guides by contest: Math Kangaroo Noetic MOEMS CML AMC 8
Free practice problems: Math Kangaroo Noetic MOEMS CML AMC 8
On this page · 6 sections
These 10 fun math logic puzzles are written for kids in grades 3 to 6. Each one practices a reasoning move that math contests reward, and every puzzle is original. The answers, with the reasoning, are all at the end, so if you print this page the puzzles come first and you can keep the answers back.
How to use them: one puzzle a day, paper and pencil, no time limit. When your child finishes, ask them to explain the answer out loud. Explaining shows whether they reasoned it out or guessed.
Which puzzle builds which skill
| Puzzles | Type | Skill it builds | Practice more with |
|---|---|---|---|
| 1–3 | Logic grids and line-ups | Using every clue, ruling options out | Clue Crew |
| 4–5 | Truth-tellers and fibbers | Testing a case and finding the contradiction | Clue Crew |
| 6 | Number pyramid | Working backward | Stack Attack |
| 7 | Cage grid | Combining arithmetic with logic | Grid Lock |
| 8 | Make the target | Flexible mental math | Hit the Target |
| 9 | Mystery number | Turning words into a number fact | Problem of the Week |
| 10 | Worst case | Guaranteeing an outcome | Problem of the Week |
Logic grid and line-up puzzles (grades 3–4)
Puzzle 1: Three pets. Ana, Ben and Cal each have one pet: a cat, a dog or a fish. Ben’s pet is not the cat. Neither Ana nor Ben has the fish. Who has which pet?
Puzzle 2: Summer reading. Dee, Eli, Fay and Gus read 2, 3, 4 and 5 books this summer, one number each.
- Eli read more books than Fay.
- Dee read an odd number of books.
- Gus read exactly one more book than Dee.
How many books did each child read?
Puzzle 3: The lunch line. Hal, Ivy, Jo, Kim and Lou stand in a line. Place 1 is the front.
- Jo is exactly in the middle.
- Kim stands directly behind Lou.
- Hal is not first and not last.
- Ivy is somewhere in front of Hal.
What is the order, front to back?
Tip: draw a grid with names down the side and choices across the top. Mark ✗ for “no” and ✓ for “yes”. When a row has one empty square left, that square is the answer.
Truth-teller puzzles (grades 4–6)
Puzzle 4: Truth-tellers and fibbers. On Puzzle Island, every person is either a truth-teller (always tells the truth) or a fibber (never tells the truth). You meet three islanders.
- Pia says: “Quinn is a fibber.”
- Quinn says: “Rex is a truth-teller.”
- Rex says: “Pia and Quinn are both fibbers.”
Who is a truth-teller and who is a fibber?
Puzzle 5: The last cookie. One of four kids ate the last cookie. Exactly one of them is telling the truth.
- Sam: “Tia ate it.”
- Tia: “Vin ate it.”
- Uma: “I didn’t eat it.”
- Vin: “Tia is not telling the truth.”
Who ate the cookie?
Number puzzles and fun math problems (grades 3–6)
Puzzle 6: Number pyramid. Every brick is the sum of the two bricks directly below it. Fill in the missing bricks.
[ 28 ]
[ ? ] [ 15 ]
[ ? ] [ 7 ] [ ? ]
[ 4 ] [ ? ] [ ? ] [ ? ]Puzzle 7: Cage grid. Fill the 4 by 4 grid with the numbers 1 to 4 so that no number repeats in any row or column. Squares with the same letter form a cage, and each cage must make its target.
| Col 1 | Col 2 | Col 3 | Col 4 | |
|---|---|---|---|---|
| Row 1 | A | B | B | C |
| Row 2 | A | D | E | C |
| Row 3 | F | D | E | G |
| Row 4 | F | F | H | G |
| Cage | Target |
|---|---|
| A | adds to 4 |
| B | adds to 5 |
| C | adds to 6 |
| D | the two numbers differ by 1 |
| E | multiplies to 2 |
| F | multiplies to 8 |
| G | adds to 4 |
| H | is 4 |
Puzzle 8: Make 100. Use the numbers 2, 3, 5, 7 and 9 with +, −, × and ÷ to make exactly 100. Use each number at most once; you don’t have to use them all. Bonus: what is the fewest numbers you can use?
Puzzle 9: Mystery number. I am a two-digit number. My digits add up to 11. If you swap my digits, the new number is 27 more than me. What number am I?
Puzzle 10: Hats in the dark. A dark closet holds 5 red hats, 4 blue hats and 3 green hats. You grab hats without looking.
- (a) How many must you grab to be sure of two hats of the same color?
- (b) How many must you grab to be sure of two red hats?
Answers
1. Cal has the fish (Ana and Ben don’t). Ben’s pet is not the cat or the fish, so Ben has the dog, and Ana has the cat.
2. Dee’s odd number is 3 or 5. Gus has one more than Dee, and nobody read 6, so Dee read 3 and Gus read 4. That leaves 2 and 5 for Eli and Fay, and Eli read more: Eli 5, Fay 2.
3. Ivy, Hal, Jo, Lou, Kim. Jo is in place 3, so Lou and Kim (side by side) fill places 1–2 or 4–5. If they took 1–2, Hal would be in 4 and Ivy in 5, behind Hal, which breaks the last clue. So Lou is 4 and Kim is 5. Hal can’t be first, so Hal is 2 and Ivy is 1.
4. Pia is a truth-teller; Quinn and Rex are fibbers. Test Rex first: if Rex told the truth, Pia and Quinn would both be fibbers. But then Quinn’s statement “Rex is a truth-teller” would be true, and a fibber can’t say something true. So Rex is a fibber. Quinn called Rex a truth-teller, which is false, so Quinn is a fibber. Pia said Quinn is a fibber, which is true, so Pia tells the truth. Check Rex: “Pia and Quinn are both fibbers” is false, as it should be.
5. Uma ate it. Try each kid as the eater and count the true statements. If Uma ate it, Sam and Tia are wrong, Uma’s “I didn’t” is false, and Vin’s statement is true (Vin didn’t eat it, so Tia is wrong). That is exactly one true statement. Every other choice gives two or three true statements: if Tia ate it, for example, Sam, Uma and Vin are all telling the truth.
6. Work backward. Top 28 minus 15 gives 13. Then 13 minus 7 gives 6, and 6 minus 4 gives 2. Next, 7 minus 2 gives 5. On the right, 15 minus 7 gives 8, and 8 minus 5 gives 3. Bottom row: 4, 2, 5, 3. Middle rows: 6, 7, 8 and 13, 15.
7.
| Col 1 | Col 2 | Col 3 | Col 4 | |
|---|---|---|---|---|
| Row 1 | 1 | 2 | 3 | 4 |
| Row 2 | 3 | 4 | 1 | 2 |
| Row 3 | 4 | 3 | 2 | 1 |
| Row 4 | 2 | 1 | 4 | 3 |
Start with H = 4. Cage E multiplies to 2, so it holds 1 and 2, and column 3 then needs 3 in row 1. Cage B: 5 − 3 = 2 in row 1, column 2. Cage G adds to 4, so it is 1 and 3, which leaves 2 and 4 for cage C; row 1 already has a 2, so row 1 ends in 4 and row 1 starts with 1. Cage A: 4 − 1 = 3. Row 2 already has 2 (cage C), so cage E’s top square is 1, row 2 column 2 is 4, and the square below the 1 is 2. Cage D differs by 1 from 4, so it is 3 (5 is too big). The rest follows from no repeats, and cage F checks: 4 × 2 × 1 = 8.
8. One way: (3 + 7) × 2 × 5 = 100, using four numbers. Other ways exist. Four is the fewest: we checked every way to combine three or fewer of the numbers, and none makes 100.
9. 47. Swapping the digits of a two-digit number changes it by 9 times the difference of its digits, so the ones digit is 3 more than the tens digit (27 ÷ 9 = 3). Two digits that add to 11 and differ by 3 are 4 and 7. Check: 74 − 47 = 27.
10. (a) 4. The unluckiest grab is one red, one blue, one green; the fourth hat must match one of them. (b) 9. The unluckiest grab is all 4 blue, all 3 green and 1 red (8 hats); the ninth hat must be red.
Keep going: a new math puzzle game every day
If your child liked these, MEC Games has five free math games with a new puzzle every day at midnight Eastern, the same one for everyone:
- Clue Crew: logic grids like Puzzles 1–3, 4 by 4 Sunday to Thursday and 5 by 5 on Friday and Saturday. Stuck? A hint points to the clue to read next.
- Stack Attack: number pyramids like Puzzle 6.
- Grid Lock: cage grids like Puzzle 7. Sunday and Monday use addition only; Friday and Saturday are 5 by 5 with all four operations.
- Hit the Target: five number tiles and a target, like Puzzle 8, with three stars for using the fewest tiles.
- Times Trail: a daily trail of times-table facts, plus practice on any table, for the quick multiplication that number puzzles lean on.
For more math puzzles for fourth graders, see math games for 4th and 5th graders. Teachers and club leaders can find ways to use these in a group in math games for the classroom and in how to start a math club.
For harder math challenges, see math games for 6th graders; the Problem of the Week sends one original contest-style problem every Sunday, and our free practice problems are sorted by grade and contest. For games sorted by grade and skill, see free math games for kids.