12 magic squares with answers
Write the numbers in the grid so that every row, every column and both diagonals add to the same total. Start on 3 × 3 squares of 1 to 9, then other numbers, then 4 × 4. Solve on screen with running totals, or print them with the answers.
Solve one on screen
Use 1 to 9 once each. Every line adds to 15.
Type a number in any empty square. Your numbers stay on this device.
12 puzzles · Magic squares with answers · answers included
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Easy: 3 × 3, numbers 1 to 9
- 1
Magic square 1: write the numbers 1 to 9 in the grid, each once, so that every row, every column and both diagonals add to 15. 3 numbers are given.
A 3 by 3 magic square with 3 numbers given.
Solve it on screeneasy
Hint: Start with row 2: it has one empty square, and it must add to 15, so that square holds 1.
AnswerEvery row, column and diagonal adds to 15.
Every step is a line with one empty square: the missing number is the total minus the numbers already in that line.
- 2
Magic square 2: write the numbers 1 to 9 in the grid, each once, so that every row, every column and both diagonals add to 15. 3 numbers are given.
A 3 by 3 magic square with 3 numbers given.
Solve it on screeneasy
Hint: Start with row 1: it has one empty square, and it must add to 15, so that square holds 6.
AnswerEvery row, column and diagonal adds to 15.
Every step is a line with one empty square: the missing number is the total minus the numbers already in that line.
- 3
Magic square 3: write the numbers 1 to 9 in the grid, each once, so that every row, every column and both diagonals add to 15. 3 numbers are given.
A 3 by 3 magic square with 3 numbers given.
Solve it on screeneasy
Hint: Start with row 1: it has one empty square, and it must add to 15, so that square holds 9.
AnswerEvery row, column and diagonal adds to 15.
Every step is a line with one empty square: the missing number is the total minus the numbers already in that line.
- 4
Magic square 4: write the numbers 1 to 9 in the grid, each once, so that every row, every column and both diagonals add to 15. 3 numbers are given.
A 3 by 3 magic square with 3 numbers given.
Solve it on screeneasy
Hint: Start with row 1: it has one empty square, and it must add to 15, so that square holds 2.
AnswerEvery row, column and diagonal adds to 15.
Every step is a line with one empty square: the missing number is the total minus the numbers already in that line.
Medium: 3 × 3, other numbers
- 5
Magic square 5: write the numbers 11 to 19 in the grid, each once, so that every row, every column and both diagonals add to 45. 2 numbers are given.
A 3 by 3 magic square with 2 numbers given.
Solve it on screenmedium
Hint: Start in the middle: in a 3 × 3 magic square the middle square always holds the middle number of the nine, here 15.
AnswerEvery row, column and diagonal adds to 45.
Lines with one empty square run out early, so the way in is the middle: the middle square of a 3 × 3 magic square always holds the middle number of the nine, a third of the total. From there each line closes in turn.
- 6
Magic square 6: write the numbers 2, 4, 6, 8, 10, 12, 14, 16 and 18 in the grid, each once, so that every row, every column and both diagonals add to 30. 2 numbers are given.
A 3 by 3 magic square with 2 numbers given.
Solve it on screenmedium
Hint: Start in the middle: in a 3 × 3 magic square the middle square always holds the middle number of the nine, here 10.
AnswerEvery row, column and diagonal adds to 30.
Lines with one empty square run out early, so the way in is the middle: the middle square of a 3 × 3 magic square always holds the middle number of the nine, a third of the total. From there each line closes in turn.
- 7
Magic square 7: write the numbers 5 to 13 in the grid, each once, so that every row, every column and both diagonals add to 27. 2 numbers are given.
A 3 by 3 magic square with 2 numbers given.
Solve it on screenmedium
Hint: Start in the middle: in a 3 × 3 magic square the middle square always holds the middle number of the nine, here 9.
AnswerEvery row, column and diagonal adds to 27.
Lines with one empty square run out early, so the way in is the middle: the middle square of a 3 × 3 magic square always holds the middle number of the nine, a third of the total. From there each line closes in turn.
- 8
Magic square 8: write the numbers 10, 20, 30, 40, 50, 60, 70, 80 and 90 in the grid, each once, so that every row, every column and both diagonals add to 150. 2 numbers are given.
A 3 by 3 magic square with 2 numbers given.
Solve it on screenmedium
Hint: Start in the middle: in a 3 × 3 magic square the middle square always holds the middle number of the nine, here 50.
AnswerEvery row, column and diagonal adds to 150.
Lines with one empty square run out early, so the way in is the middle: the middle square of a 3 × 3 magic square always holds the middle number of the nine, a third of the total. From there each line closes in turn.
Hard: 4 × 4, numbers 1 to 16
- 9
Magic square 9: write the numbers 1 to 16 in the grid, each once, so that every row, every column and both diagonals add to 34. 8 numbers are given.
A 4 by 4 magic square with 8 numbers given.
Solve it on screenhard
Hint: Start with row 1: it has one empty square, and it must add to 34, so that square holds 13.
AnswerEvery row, column and diagonal adds to 34.
Every row, column and diagonal of a 4 × 4 square of 1 to 16 adds to 34. Fill a line with one empty square, and the next one opens.
- 10
Magic square 10: write the numbers 1 to 16 in the grid, each once, so that every row, every column and both diagonals add to 34. 8 numbers are given.
A 4 by 4 magic square with 8 numbers given.
Solve it on screenhard
Hint: Start with row 3: it has one empty square, and it must add to 34, so that square holds 1.
AnswerEvery row, column and diagonal adds to 34.
Every row, column and diagonal of a 4 × 4 square of 1 to 16 adds to 34. Fill a line with one empty square, and the next one opens.
- 11
Magic square 11: write the numbers 1 to 16 in the grid, each once, so that every row, every column and both diagonals add to 34. 8 numbers are given.
A 4 by 4 magic square with 8 numbers given.
Solve it on screenhard
Hint: Start with row 1: it has one empty square, and it must add to 34, so that square holds 15.
AnswerEvery row, column and diagonal adds to 34.
Every row, column and diagonal of a 4 × 4 square of 1 to 16 adds to 34. Fill a line with one empty square, and the next one opens.
- 12
Magic square 12: write the numbers 1 to 16 in the grid, each once, so that every row, every column and both diagonals add to 34. 8 numbers are given.
A 4 by 4 magic square with 8 numbers given.
Solve it on screenhard
Hint: Start with row 2: it has one empty square, and it must add to 34, so that square holds 12.
AnswerEvery row, column and diagonal adds to 34.
Every row, column and diagonal of a 4 × 4 square of 1 to 16 adds to 34. Fill a line with one empty square, and the next one opens.
Timer and team scores
8 turns × 60 seconds = 8 minutes of play, plus instructions and breaks.
60
Pause whenever the group needs more time.
Team Lime's turn
Team Lime: 0
Team Violet: 0
Team Tangerine: 0
Team Sky: 0
Team Lemon: 0
Team Bubblegum: 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.