Magic Square 4×4 Hard — Set 81
This page uses a content type that does not have a custom renderer yet. Raw structured data is shown below.
{
"contentData": {
"operation": "magic-square",
"subject": "arithmetic",
"difficulty": "hard",
"gridSize": 4,
"config": {
"gridSize": 4,
"difficulty": "hard",
"maxNumber": 10
},
"problems": [
{
"type": "magic-square",
"subType": "magic-square",
"difficulty": "hard",
"question": "Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [5 _ _ | _ _ 6 | 9 _ _]",
"answer": "5 12 7 | 10 8 6 | 9 4 11",
"grid": [
[
5,
null,
null
],
[
null,
null,
6
],
[
9,
null,
null
]
],
"solvedGrid": [
[
5,
12,
7
],
[
10,
8,
6
],
[
9,
4,
11
]
],
"magicConstant": 24
},
{
"type": "magic-square",
"subType": "magic-square",
"difficulty": "hard",
"question": "Complete the magic square. Each row, column, and diagonal must sum to 15. Grid: [_ _ 6 | _ 5 _ | _ 3 _]",
"answer": "2 7 6 | 9 5 1 | 4 3 8",
"grid": [
[
null,
null,
6
],
[
null,
5,
null
],
[
null,
3,
null
]
],
"solvedGrid": [
[
2,
7,
6
],
[
9,
5,
1
],
[
4,
3,
8
]
],
"magicConstant": 15
},
{
"type": "magic-square",
"subType": "magic-square",
"difficulty": "hard",
"question": "Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [_ _ 7 | 10 _ _ | 9 _ _]",
"answer": "5 12 7 | 10 8 6 | 9 4 11",
"grid": [
[
null,
null,
7
],
[
10,
null,
null
],
[
9,
null,
null
]
],
"solvedGrid": [
[
5,
12,
7
],
[
10,
8,
6
],
[
9,
4,
11
]
],
"magicConstant": 24
},
{
"type": "magic-square",
"subType": "magic-square",
"difficulty": "hard",
"question": "Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [_ _ _ | 6 _ 10 | 7 _ _]",
"answer": "11 4 9 | 6 8 10 | 7 12 5",
"grid": [
[
null,
null,
null
],
[
6,
null,
10
],
[
7,
null,
null
]
],
"solvedGrid": [
[
11,
4,
9
],
[
6,
8,
10
],
[
7,
12,
5
]
],
"magicConstant": 24
}
],
"layout": {
"columns": 2,
"problemsPerPage": 20
}
},
"outputTargets": {
"screen": true,
"print": true,
"pdf": true,
"answerKey": true
},
"_archetype": "form-exercise",
"_generatorId": "arithmetic-generator-v7.2.1"
}Teaching Notes
- Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [5 _ _ | _ _ 6 | 9 _ _]
- Complete the magic square. Each row, column, and diagonal must sum to 15. Grid: [_ _ 6 | _ 5 _ | _ 3 _]
- Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [_ _ 7 | 10 _ _ | 9 _ _]
- Complete the magic square. Each row, column, and diagonal must sum to 24. Grid: [_ _ _ | 6 _ 10 | 7 _ _]
Practice magic square 4x4 with free printable worksheets. Uniquely generated — reinforce key math skills with every set.
Frequently Asked Questions
How do I use this Magic Square 4x4 Hard Worksheets worksheet?
Print the worksheet and complete the problems. Each set number generates a unique arrangement. Use the same set number for all students in a class for consistent assessment.
Is there an answer key?
Yes — every worksheet includes a complete answer key. Print it separately or view it on screen.