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From a story to your own conjecture

Problem stories open curiosity. The problem workshop is the next place, where curiosity becomes a testable idea.

1 · DiscoverMeet the questionLearn when it appeared and why it still holds people’s attention.
2 · ChallengeTest one caseMake your first observation in five minutes with a drawing, calculation, or colors.
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Week 13 · ErdősOpen

Magic Square of Squares — Can 3×3 Be Done?

Simple rule · open problem· Posed 1996

Problem

Is there a $3\times 3$ magic square (rows, columns, diagonals all sum to the same value) whose nine entries are distinct positive perfect squares?

Why it matters

Martin Gardner popularized this with a $100 prize in 1996. Andrew Bremner that year showed a near-miss where 7 of 8 sums match. Computer search has covered all sum-values below$ 10^{14} $with no positive result. A$ 10{,}000 prize is now on offer for a true solution.

Progress so far

Bremner (1996) and Boyer (2005) found near-misses where 7 of 8 sums match. Robertson (2010) showed rational solutions exist but no integer-square solution has been found. As of 2025, exhaustive computer search has ruled out all 8-tuples up to large bounds.

💡 Explore together, one line at a time(0 contributions)

Contributions are not ranked by popularity. Curator feedback names what is clear or reproducible, and peer signals mean someone understood or actually reproduced it.

What did you notice?

You do not need a complete proof. A small observation can open the next path.

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