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 40. One row has 20, 16, and ____. What is the missing number?
40 · 20 · 16 · Magic square missing values
2. In a magic square, every row adds up to 17. One row has 3, 6, and ____. What is the missing number?
17 · 3 · 6 · Magic square missing values
3. In a magic square, every row adds up to 28. One row has 5, 13, and ____. What is the missing number?
28 · 5 · 13 · Magic square missing values
4. In a magic square, every row adds up to 17. One row has 8, 6, and ____. What is the missing number?
17 · 8 · 6 · Magic square missing values
5. In a magic square, every row adds up to 42. One row has 12, 20, and ____. What is the missing number?
42 · 12 · 20 · Magic square missing values
6. In a magic square, every row adds up to 45. One row has 15, 13, and ____. What is the missing number?
45 · 15 · 13 · Magic square missing values
7. In a magic square, every row adds up to 35. One row has 10, 8, and ____. What is the missing number?
35 · 10 · 8 · Magic square missing values
8. In a magic square, every row adds up to 32. One row has 15, 4, and ____. What is the missing number?
32 · 15 · 4 · Magic square missing values
9. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
31 · 6 · 16 · Magic square missing values
10. In a magic square, every row adds up to 24. One row has 4, 6, and ____. What is the missing number?
24 · 4 · 6 · Magic square missing values
11. In a magic square, every row adds up to 45. One row has 19, 12, and ____. What is the missing number?
45 · 19 · 12 · Magic square missing values
12. In a magic square, every row adds up to 14. One row has 8, 3, and ____. What is the missing number?
14 · 8 · 3 · Magic square missing values

12 questions · Seed 104737 · 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 40. One row has 20, 16, and ____. What is the missing number?
4
Subtract 20 + 16 = 36 from 40: 40 − 36 = 4.
2. In a magic square, every row adds up to 17. One row has 3, 6, and ____. What is the missing number?
8
Subtract 3 + 6 = 9 from 17: 17 − 9 = 8.
3. In a magic square, every row adds up to 28. One row has 5, 13, and ____. What is the missing number?
10
Subtract 5 + 13 = 18 from 28: 28 − 18 = 10.
4. In a magic square, every row adds up to 17. One row has 8, 6, and ____. What is the missing number?
3
Subtract 8 + 6 = 14 from 17: 17 − 14 = 3.
5. In a magic square, every row adds up to 42. One row has 12, 20, and ____. What is the missing number?
10
Subtract 12 + 20 = 32 from 42: 42 − 32 = 10.
6. In a magic square, every row adds up to 45. One row has 15, 13, and ____. What is the missing number?
17
Subtract 15 + 13 = 28 from 45: 45 − 28 = 17.
7. In a magic square, every row adds up to 35. One row has 10, 8, and ____. What is the missing number?
17
Subtract 10 + 8 = 18 from 35: 35 − 18 = 17.
8. In a magic square, every row adds up to 32. One row has 15, 4, and ____. What is the missing number?
13
Subtract 15 + 4 = 19 from 32: 32 − 19 = 13.
9. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
9
Subtract 6 + 16 = 22 from 31: 31 − 22 = 9.
10. In a magic square, every row adds up to 24. One row has 4, 6, and ____. What is the missing number?
14
Subtract 4 + 6 = 10 from 24: 24 − 10 = 14.
11. In a magic square, every row adds up to 45. One row has 19, 12, and ____. What is the missing number?
14
Subtract 19 + 12 = 31 from 45: 45 − 31 = 14.
12. In a magic square, every row adds up to 14. One row has 8, 3, and ____. What is the missing number?
3
Subtract 8 + 3 = 11 from 14: 14 − 11 = 3.

12 questions · Seed 104737 · 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 40. One row has 20, 16, and ____. What is the missing number?
40 · 20 · 16 · Magic square missing values
2. In a magic square, every row adds up to 17. One row has 3, 6, and ____. What is the missing number?
17 · 3 · 6 · Magic square missing values
3. In a magic square, every row adds up to 28. One row has 5, 13, and ____. What is the missing number?
28 · 5 · 13 · Magic square missing values
4. In a magic square, every row adds up to 17. One row has 8, 6, and ____. What is the missing number?
17 · 8 · 6 · Magic square missing values
5. In a magic square, every row adds up to 42. One row has 12, 20, and ____. What is the missing number?
42 · 12 · 20 · Magic square missing values
6. In a magic square, every row adds up to 45. One row has 15, 13, and ____. What is the missing number?
45 · 15 · 13 · Magic square missing values
7. In a magic square, every row adds up to 35. One row has 10, 8, and ____. What is the missing number?
35 · 10 · 8 · Magic square missing values
8. In a magic square, every row adds up to 32. One row has 15, 4, and ____. What is the missing number?
32 · 15 · 4 · Magic square missing values
9. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
31 · 6 · 16 · Magic square missing values
10. In a magic square, every row adds up to 24. One row has 4, 6, and ____. What is the missing number?
24 · 4 · 6 · Magic square missing values
11. In a magic square, every row adds up to 45. One row has 19, 12, and ____. What is the missing number?
45 · 19 · 12 · Magic square missing values
12. In a magic square, every row adds up to 14. One row has 8, 3, and ____. What is the missing number?
14 · 8 · 3 · Magic square missing values

12 questions · Seed 104737 · 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 40. One row has 20, 16, and ____. What is the missing number?
4
Subtract 20 + 16 = 36 from 40: 40 − 36 = 4.
2. In a magic square, every row adds up to 17. One row has 3, 6, and ____. What is the missing number?
8
Subtract 3 + 6 = 9 from 17: 17 − 9 = 8.
3. In a magic square, every row adds up to 28. One row has 5, 13, and ____. What is the missing number?
10
Subtract 5 + 13 = 18 from 28: 28 − 18 = 10.
4. In a magic square, every row adds up to 17. One row has 8, 6, and ____. What is the missing number?
3
Subtract 8 + 6 = 14 from 17: 17 − 14 = 3.
5. In a magic square, every row adds up to 42. One row has 12, 20, and ____. What is the missing number?
10
Subtract 12 + 20 = 32 from 42: 42 − 32 = 10.
6. In a magic square, every row adds up to 45. One row has 15, 13, and ____. What is the missing number?
17
Subtract 15 + 13 = 28 from 45: 45 − 28 = 17.
7. In a magic square, every row adds up to 35. One row has 10, 8, and ____. What is the missing number?
17
Subtract 10 + 8 = 18 from 35: 35 − 18 = 17.
8. In a magic square, every row adds up to 32. One row has 15, 4, and ____. What is the missing number?
13
Subtract 15 + 4 = 19 from 32: 32 − 19 = 13.
9. In a magic square, every row adds up to 31. One row has 6, 16, and ____. What is the missing number?
9
Subtract 6 + 16 = 22 from 31: 31 − 22 = 9.
10. In a magic square, every row adds up to 24. One row has 4, 6, and ____. What is the missing number?
14
Subtract 4 + 6 = 10 from 24: 24 − 10 = 14.
11. In a magic square, every row adds up to 45. One row has 19, 12, and ____. What is the missing number?
14
Subtract 19 + 12 = 31 from 45: 45 − 31 = 14.
12. In a magic square, every row adds up to 14. One row has 8, 3, and ____. What is the missing number?
3
Subtract 8 + 3 = 11 from 14: 14 − 11 = 3.

12 questions · Seed 104737 · Age guidance, not curriculum certification