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Odd-Order Magic Square Generator — result sheet
Generate the classic odd-order normal magic square and verify its common row, column, and diagonal sum.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Normal magic constant M = n(n² + 1) / 2; the Siamese construction places 1 in the top-middle and wraps diagonal moves with collision fallback.
A normal magic square uses every integer from 1 through n² exactly once, with equal sums on every row, column, and main diagonal. The generator uses the standard odd-order Siamese construction and returns the actual grid for inspection.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Square order — Use an odd order from 3 through 15.; minimum 3; maximum 15
Worked example
| Input | Value |
|---|---|
| Square order | 3 |
8 1 6 / 3 5 7 / 4 9 2; magic constant 15
Assumptions and limits
- The order is an odd integer from 3 through 15; even-order construction is not silently substituted.
- The square is the normal integer construction using 1 through n².
- The result is a mathematical pattern, not a claim of randomness, uniqueness, or a puzzle solution for arbitrary clues.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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