Magic Square 5×5 Hard — Set 85

This page uses a content type that does not have a custom renderer yet. Raw structured data is shown below.

{
    "_meta": {
        "nodeId": "node-1-leaf-magic-square-5x5-hard",
        "pageNumber": 85,
        "generatedAt": "2026-03-16T15:22:01.214Z",
        "generatorVersion": "v7.2.1-wp-g2",
        "seed": "221ac7c2aaa86b2a",
        "seedInput": "1|node-1-leaf-magic-square-5x5-hard|85|1.0.0|",
        "schemaVersion": "2.0.0",
        "mathTemplateId": null,
        "archetype": "form-exercise",
        "siteId": 1
    },
    "semantics": {
        "solvability": {
            "isDeterministic": true,
            "solutionCount": 1
        },
        "difficulty": {
            "declaredLevel": "hard",
            "computedScore": 18,
            "metrics": {
                "problemCount": 4,
                "operation": "magic-square",
                "digits": 2,
                "regrouping": false
            }
        },
        "diversity": {
            "structuralHash": "b561ffddb4091138e540d36399321e87",
            "contentFingerprint": "1c4b29bb44b9703a"
        },
        "interaction": {
            "checkable": true,
            "revealable": true,
            "randomizable": true,
            "hintable": false,
            "progressable": true,
            "inputType": [
                "text-input"
            ]
        }
    },
    "version": "2.0",
    "generatorId": "arithmetic-generator-v7.2.1",
    "operation": "magic-square",
    "subject": "arithmetic",
    "difficulty": "hard",
    "gridSize": 5,
    "config": {
        "gridSize": 5,
        "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 15. Grid: [_ _ _ | 1 _ _ | _ 7 2]",
            "answer": "8 3 4 | 1 5 9 | 6 7 2",
            "grid": [
                [
                    null,
                    null,
                    null
                ],
                [
                    1,
                    null,
                    null
                ],
                [
                    null,
                    7,
                    2
                ]
            ],
            "solvedGrid": [
                [
                    8,
                    3,
                    4
                ],
                [
                    1,
                    5,
                    9
                ],
                [
                    6,
                    7,
                    2
                ]
            ],
            "magicConstant": 15
        },
        {
            "type": "magic-square",
            "subType": "magic-square",
            "difficulty": "hard",
            "question": "Complete the magic square. Each row, column, and diagonal must sum to 15. Grid: [8 _ _ | _ _ 7 | 4 _ _]",
            "answer": "8 1 6 | 3 5 7 | 4 9 2",
            "grid": [
                [
                    8,
                    null,
                    null
                ],
                [
                    null,
                    null,
                    7
                ],
                [
                    4,
                    null,
                    null
                ]
            ],
            "solvedGrid": [
                [
                    8,
                    1,
                    6
                ],
                [
                    3,
                    5,
                    7
                ],
                [
                    4,
                    9,
                    2
                ]
            ],
            "magicConstant": 15
        },
        {
            "type": "magic-square",
            "subType": "magic-square",
            "difficulty": "hard",
            "question": "Complete the magic square. Each row, column, and diagonal must sum to 33. Grid: [_ _ 10 | 13 _ _ | 12 _ _]",
            "answer": "8 15 10 | 13 11 9 | 12 7 14",
            "grid": [
                [
                    null,
                    null,
                    10
                ],
                [
                    13,
                    null,
                    null
                ],
                [
                    12,
                    null,
                    null
                ]
            ],
            "solvedGrid": [
                [
                    8,
                    15,
                    10
                ],
                [
                    13,
                    11,
                    9
                ],
                [
                    12,
                    7,
                    14
                ]
            ],
            "magicConstant": 33
        },
        {
            "type": "magic-square",
            "subType": "magic-square",
            "difficulty": "hard",
            "question": "Complete the magic square. Each row, column, and diagonal must sum to 15. Grid: [_ 7 _ | 9 _ _ | _ _ 8]",
            "answer": "2 7 6 | 9 5 1 | 4 3 8",
            "grid": [
                [
                    null,
                    7,
                    null
                ],
                [
                    9,
                    null,
                    null
                ],
                [
                    null,
                    null,
                    8
                ]
            ],
            "solvedGrid": [
                [
                    2,
                    7,
                    6
                ],
                [
                    9,
                    5,
                    1
                ],
                [
                    4,
                    3,
                    8
                ]
            ],
            "magicConstant": 15
        }
    ],
    "layout": {
        "columns": 2,
        "problemsPerPage": 20
    },
    "_archetype": "form-exercise",
    "_generatorId": "arithmetic-generator-v7.2.1"
}