Inder J. Taneja · Recreational Mathematics

Magic-Bimagic-Trimagic-Tetramagic-Pentamagic
Square Checker

One square. Five levels of verification.

Exact sums · Powers 1–5 · Entry-set analysis · Block checks

Choose your square

Or drag a file here. File checking runs locally in your browser.

One row per line. Separate integers with spaces, tabs, commas or semicolons. Lines starting with # are ignored. Use plain integer digits without thousands separators.

Must divide the complete order. Each aligned block is checked against its own line sums.

Ready for a square.

Try a verified example

Start small, then compare the five levels.

What do the five levels mean?

A square is magic when its rows, columns and both principal diagonals share one sum. Bimagic also requires equal sums of squares; trimagic adds cubes; tetramagic adds fourth powers; pentamagic adds fifth powers.

Each level includes all preceding levels. Equal fifth-power sums alone do not establish pentamagicity.

Normality and large files

Normality means each integer from 1 through N² occurs exactly once. Consecutive entries can start at any integer, including 0 or a negative value. Sequential here describes the entry set, not the order of entries in each row. The report also shows repetitions and missing integers between the minimum and maximum.

Files are read in chunks, and calculations run in a background worker. The checker retains column sums rather than the whole matrix. Very large files can take considerable time; Cancel stops the calculation. Normality is checked for up to 500 million entries. Shifted and non-normal inputs receive an additional entry-set pass. Extremely sparse ranges with over one million distinct values are clearly marked as only partially checked.

Credits and mathematical sources

Checker and presentation: Inder J. Taneja. Example seeds: Georges Pfeffermann (order 8), Walter Trump (order 12), and Toshihiro Shirakawa (orders 64 and 512). The Shirakawa examples are normalized to start at 1 when needed.

Pfeffermann numerical record · Walter Trump’s trimagic squares · Toshihiro Shirakawa’s collection · Christian Boyer’s Multimagie.com