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 36. One row has 12, 4, and ____. What is the missing number?
36 · 12 · 4 · Magic square missing values
2. In a magic square, every row adds up to 39. One row has 16, 5, and ____. What is the missing number?
39 · 16 · 5 · Magic square missing values
3. In a magic square, every row adds up to 22. One row has 5, 10, and ____. What is the missing number?
22 · 5 · 10 · Magic square missing values
4. In a magic square, every row adds up to 34. One row has 3, 18, and ____. What is the missing number?
34 · 3 · 18 · Magic square missing values
5. In a magic square, every row adds up to 41. One row has 20, 16, and ____. What is the missing number?
41 · 20 · 16 · Magic square missing values
6. In a magic square, every row adds up to 38. One row has 8, 19, and ____. What is the missing number?
38 · 8 · 19 · Magic square missing values
7. In a magic square, every row adds up to 44. One row has 10, 20, and ____. What is the missing number?
44 · 10 · 20 · Magic square missing values
8. In a magic square, every row adds up to 42. One row has 4, 19, and ____. What is the missing number?
42 · 4 · 19 · Magic square missing values
9. In a magic square, every row adds up to 39. One row has 7, 17, and ____. What is the missing number?
39 · 7 · 17 · Magic square missing values
10. In a magic square, every row adds up to 51. One row has 18, 15, and ____. What is the missing number?
51 · 18 · 15 · Magic square missing values
11. In a magic square, every row adds up to 24. One row has 11, 9, and ____. What is the missing number?
24 · 11 · 9 · Magic square missing values
12. In a magic square, every row adds up to 30. One row has 10, 10, and ____. What is the missing number?
30 · 10 · 10 · Magic square missing values

12 questions · Seed 73 · 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 36. One row has 12, 4, and ____. What is the missing number?
20
Subtract 12 + 4 = 16 from 36: 36 − 16 = 20.
2. In a magic square, every row adds up to 39. One row has 16, 5, and ____. What is the missing number?
18
Subtract 16 + 5 = 21 from 39: 39 − 21 = 18.
3. In a magic square, every row adds up to 22. One row has 5, 10, and ____. What is the missing number?
7
Subtract 5 + 10 = 15 from 22: 22 − 15 = 7.
4. In a magic square, every row adds up to 34. One row has 3, 18, and ____. What is the missing number?
13
Subtract 3 + 18 = 21 from 34: 34 − 21 = 13.
5. In a magic square, every row adds up to 41. One row has 20, 16, and ____. What is the missing number?
5
Subtract 20 + 16 = 36 from 41: 41 − 36 = 5.
6. In a magic square, every row adds up to 38. One row has 8, 19, and ____. What is the missing number?
11
Subtract 8 + 19 = 27 from 38: 38 − 27 = 11.
7. In a magic square, every row adds up to 44. One row has 10, 20, and ____. What is the missing number?
14
Subtract 10 + 20 = 30 from 44: 44 − 30 = 14.
8. In a magic square, every row adds up to 42. One row has 4, 19, and ____. What is the missing number?
19
Subtract 4 + 19 = 23 from 42: 42 − 23 = 19.
9. In a magic square, every row adds up to 39. One row has 7, 17, and ____. What is the missing number?
15
Subtract 7 + 17 = 24 from 39: 39 − 24 = 15.
10. In a magic square, every row adds up to 51. One row has 18, 15, and ____. What is the missing number?
18
Subtract 18 + 15 = 33 from 51: 51 − 33 = 18.
11. In a magic square, every row adds up to 24. One row has 11, 9, and ____. What is the missing number?
4
Subtract 11 + 9 = 20 from 24: 24 − 20 = 4.
12. In a magic square, every row adds up to 30. One row has 10, 10, and ____. What is the missing number?
10
Subtract 10 + 10 = 20 from 30: 30 − 20 = 10.

12 questions · Seed 73 · 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 36. One row has 12, 4, and ____. What is the missing number?
36 · 12 · 4 · Magic square missing values
2. In a magic square, every row adds up to 39. One row has 16, 5, and ____. What is the missing number?
39 · 16 · 5 · Magic square missing values
3. In a magic square, every row adds up to 22. One row has 5, 10, and ____. What is the missing number?
22 · 5 · 10 · Magic square missing values
4. In a magic square, every row adds up to 34. One row has 3, 18, and ____. What is the missing number?
34 · 3 · 18 · Magic square missing values
5. In a magic square, every row adds up to 41. One row has 20, 16, and ____. What is the missing number?
41 · 20 · 16 · Magic square missing values
6. In a magic square, every row adds up to 38. One row has 8, 19, and ____. What is the missing number?
38 · 8 · 19 · Magic square missing values
7. In a magic square, every row adds up to 44. One row has 10, 20, and ____. What is the missing number?
44 · 10 · 20 · Magic square missing values
8. In a magic square, every row adds up to 42. One row has 4, 19, and ____. What is the missing number?
42 · 4 · 19 · Magic square missing values
9. In a magic square, every row adds up to 39. One row has 7, 17, and ____. What is the missing number?
39 · 7 · 17 · Magic square missing values
10. In a magic square, every row adds up to 51. One row has 18, 15, and ____. What is the missing number?
51 · 18 · 15 · Magic square missing values
11. In a magic square, every row adds up to 24. One row has 11, 9, and ____. What is the missing number?
24 · 11 · 9 · Magic square missing values
12. In a magic square, every row adds up to 30. One row has 10, 10, and ____. What is the missing number?
30 · 10 · 10 · Magic square missing values

12 questions · Seed 73 · 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 36. One row has 12, 4, and ____. What is the missing number?
20
Subtract 12 + 4 = 16 from 36: 36 − 16 = 20.
2. In a magic square, every row adds up to 39. One row has 16, 5, and ____. What is the missing number?
18
Subtract 16 + 5 = 21 from 39: 39 − 21 = 18.
3. In a magic square, every row adds up to 22. One row has 5, 10, and ____. What is the missing number?
7
Subtract 5 + 10 = 15 from 22: 22 − 15 = 7.
4. In a magic square, every row adds up to 34. One row has 3, 18, and ____. What is the missing number?
13
Subtract 3 + 18 = 21 from 34: 34 − 21 = 13.
5. In a magic square, every row adds up to 41. One row has 20, 16, and ____. What is the missing number?
5
Subtract 20 + 16 = 36 from 41: 41 − 36 = 5.
6. In a magic square, every row adds up to 38. One row has 8, 19, and ____. What is the missing number?
11
Subtract 8 + 19 = 27 from 38: 38 − 27 = 11.
7. In a magic square, every row adds up to 44. One row has 10, 20, and ____. What is the missing number?
14
Subtract 10 + 20 = 30 from 44: 44 − 30 = 14.
8. In a magic square, every row adds up to 42. One row has 4, 19, and ____. What is the missing number?
19
Subtract 4 + 19 = 23 from 42: 42 − 23 = 19.
9. In a magic square, every row adds up to 39. One row has 7, 17, and ____. What is the missing number?
15
Subtract 7 + 17 = 24 from 39: 39 − 24 = 15.
10. In a magic square, every row adds up to 51. One row has 18, 15, and ____. What is the missing number?
18
Subtract 18 + 15 = 33 from 51: 51 − 33 = 18.
11. In a magic square, every row adds up to 24. One row has 11, 9, and ____. What is the missing number?
4
Subtract 11 + 9 = 20 from 24: 24 − 20 = 4.
12. In a magic square, every row adds up to 30. One row has 10, 10, and ____. What is the missing number?
10
Subtract 10 + 10 = 20 from 30: 30 − 20 = 10.

12 questions · Seed 73 · Age guidance, not curriculum certification