ReasoningAges 10-12

Magic square missing values

Use the constant row sum of a 3 × 3 magic square to deduce the missing cell value. Review suitability for your learners before teaching.

New variation Try interactive challenge Browse templates

Age band:Ages 7-9 Ages 10-12

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 10-12

Magic square missing values

Take your time. Show your thinking.

1. In a magic square, every row adds up to 38. One row has 7, 18, and ____. What is the missing number?
38 · 7 · 18 · Magic square missing values
2. In a magic square, every row adds up to 29. One row has 10, 17, and ____. What is the missing number?
29 · 10 · 17 · Magic square missing values
3. In a magic square, every row adds up to 30. One row has 7, 10, and ____. What is the missing number?
30 · 7 · 10 · Magic square missing values
4. In a magic square, every row adds up to 24. One row has 3, 7, and ____. What is the missing number?
24 · 3 · 7 · Magic square missing values
5. In a magic square, every row adds up to 29. One row has 12, 15, and ____. What is the missing number?
29 · 12 · 15 · Magic square missing values
6. In a magic square, every row adds up to 44. One row has 11, 17, and ____. What is the missing number?
44 · 11 · 17 · Magic square missing values
7. In a magic square, every row adds up to 45. One row has 6, 20, and ____. What is the missing number?
45 · 6 · 20 · Magic square missing values
8. In a magic square, every row adds up to 39. One row has 13, 14, and ____. What is the missing number?
39 · 13 · 14 · Magic square missing values
9. In a magic square, every row adds up to 37. One row has 17, 13, and ____. What is the missing number?
37 · 17 · 13 · Magic square missing values
10. In a magic square, every row adds up to 28. One row has 5, 14, and ____. What is the missing number?
28 · 5 · 14 · Magic square missing values
11. In a magic square, every row adds up to 23. One row has 13, 5, and ____. What is the missing number?
23 · 13 · 5 · Magic square missing values
12. In a magic square, every row adds up to 46. One row has 8, 18, and ____. What is the missing number?
46 · 8 · 18 · Magic square missing values

12 questions · Seed 86 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 10-12

Magic square missing values

Answers and reasoning. Review before teaching.

1. In a magic square, every row adds up to 38. One row has 7, 18, and ____. What is the missing number?
13
Subtract 7 + 18 = 25 from 38: 38 − 25 = 13.
2. In a magic square, every row adds up to 29. One row has 10, 17, and ____. What is the missing number?
2
Subtract 10 + 17 = 27 from 29: 29 − 27 = 2.
3. In a magic square, every row adds up to 30. One row has 7, 10, and ____. What is the missing number?
13
Subtract 7 + 10 = 17 from 30: 30 − 17 = 13.
4. In a magic square, every row adds up to 24. One row has 3, 7, and ____. What is the missing number?
14
Subtract 3 + 7 = 10 from 24: 24 − 10 = 14.
5. In a magic square, every row adds up to 29. One row has 12, 15, and ____. What is the missing number?
2
Subtract 12 + 15 = 27 from 29: 29 − 27 = 2.
6. In a magic square, every row adds up to 44. One row has 11, 17, and ____. What is the missing number?
16
Subtract 11 + 17 = 28 from 44: 44 − 28 = 16.
7. In a magic square, every row adds up to 45. One row has 6, 20, and ____. What is the missing number?
19
Subtract 6 + 20 = 26 from 45: 45 − 26 = 19.
8. In a magic square, every row adds up to 39. One row has 13, 14, and ____. What is the missing number?
12
Subtract 13 + 14 = 27 from 39: 39 − 27 = 12.
9. In a magic square, every row adds up to 37. One row has 17, 13, and ____. What is the missing number?
7
Subtract 17 + 13 = 30 from 37: 37 − 30 = 7.
10. In a magic square, every row adds up to 28. One row has 5, 14, and ____. What is the missing number?
9
Subtract 5 + 14 = 19 from 28: 28 − 19 = 9.
11. In a magic square, every row adds up to 23. One row has 13, 5, and ____. What is the missing number?
5
Subtract 13 + 5 = 18 from 23: 23 − 18 = 5.
12. In a magic square, every row adds up to 46. One row has 8, 18, and ____. What is the missing number?
20
Subtract 8 + 18 = 26 from 46: 46 − 26 = 20.

12 questions · Seed 86 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 10-12

Magic square missing values

Take your time. Show your thinking.

1. In a magic square, every row adds up to 38. One row has 7, 18, and ____. What is the missing number?
38 · 7 · 18 · Magic square missing values
2. In a magic square, every row adds up to 29. One row has 10, 17, and ____. What is the missing number?
29 · 10 · 17 · Magic square missing values
3. In a magic square, every row adds up to 30. One row has 7, 10, and ____. What is the missing number?
30 · 7 · 10 · Magic square missing values
4. In a magic square, every row adds up to 24. One row has 3, 7, and ____. What is the missing number?
24 · 3 · 7 · Magic square missing values
5. In a magic square, every row adds up to 29. One row has 12, 15, and ____. What is the missing number?
29 · 12 · 15 · Magic square missing values
6. In a magic square, every row adds up to 44. One row has 11, 17, and ____. What is the missing number?
44 · 11 · 17 · Magic square missing values
7. In a magic square, every row adds up to 45. One row has 6, 20, and ____. What is the missing number?
45 · 6 · 20 · Magic square missing values
8. In a magic square, every row adds up to 39. One row has 13, 14, and ____. What is the missing number?
39 · 13 · 14 · Magic square missing values
9. In a magic square, every row adds up to 37. One row has 17, 13, and ____. What is the missing number?
37 · 17 · 13 · Magic square missing values
10. In a magic square, every row adds up to 28. One row has 5, 14, and ____. What is the missing number?
28 · 5 · 14 · Magic square missing values
11. In a magic square, every row adds up to 23. One row has 13, 5, and ____. What is the missing number?
23 · 13 · 5 · Magic square missing values
12. In a magic square, every row adds up to 46. One row has 8, 18, and ____. What is the missing number?
46 · 8 · 18 · Magic square missing values

12 questions · Seed 86 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 10-12

Magic square missing values

Answers and reasoning. Review before teaching.

1. In a magic square, every row adds up to 38. One row has 7, 18, and ____. What is the missing number?
13
Subtract 7 + 18 = 25 from 38: 38 − 25 = 13.
2. In a magic square, every row adds up to 29. One row has 10, 17, and ____. What is the missing number?
2
Subtract 10 + 17 = 27 from 29: 29 − 27 = 2.
3. In a magic square, every row adds up to 30. One row has 7, 10, and ____. What is the missing number?
13
Subtract 7 + 10 = 17 from 30: 30 − 17 = 13.
4. In a magic square, every row adds up to 24. One row has 3, 7, and ____. What is the missing number?
14
Subtract 3 + 7 = 10 from 24: 24 − 10 = 14.
5. In a magic square, every row adds up to 29. One row has 12, 15, and ____. What is the missing number?
2
Subtract 12 + 15 = 27 from 29: 29 − 27 = 2.
6. In a magic square, every row adds up to 44. One row has 11, 17, and ____. What is the missing number?
16
Subtract 11 + 17 = 28 from 44: 44 − 28 = 16.
7. In a magic square, every row adds up to 45. One row has 6, 20, and ____. What is the missing number?
19
Subtract 6 + 20 = 26 from 45: 45 − 26 = 19.
8. In a magic square, every row adds up to 39. One row has 13, 14, and ____. What is the missing number?
12
Subtract 13 + 14 = 27 from 39: 39 − 27 = 12.
9. In a magic square, every row adds up to 37. One row has 17, 13, and ____. What is the missing number?
7
Subtract 17 + 13 = 30 from 37: 37 − 30 = 7.
10. In a magic square, every row adds up to 28. One row has 5, 14, and ____. What is the missing number?
9
Subtract 5 + 14 = 19 from 28: 28 − 19 = 9.
11. In a magic square, every row adds up to 23. One row has 13, 5, and ____. What is the missing number?
5
Subtract 13 + 5 = 18 from 23: 23 − 18 = 5.
12. In a magic square, every row adds up to 46. One row has 8, 18, and ____. What is the missing number?
20
Subtract 8 + 18 = 26 from 46: 46 − 26 = 20.

12 questions · Seed 86 · Age guidance, not curriculum certification