PPL 008 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
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Prize Problem LedgerBoyer magic-square enigmasPPL 008Boyer enigma #2 · 5×5 bimagic square with distinct positive integers

Permanent problem IDPPL 008

Reconfirm sponsorIndependentexistence

Recreational mathematics

Boyer enigma #2 · 5×5 bimagic square with distinct positive integers

Construct a 5×5 square of distinct positive integers whose rows, columns and main diagonals have equal sums both before and after every entry is squared, or prove impossibility.

magic squaresDiophantine equationsconstruction
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The problem

Construct a 5×5 square of distinct positive integers whose rows, columns and main diagonals have equal sums both before and after every entry is squared, or prove impossibility.

Open since2010cash contest launched
Last checked2026.07.27Catalog verification
02

Reward offers

Offer 01€1,000Christian Boyer
Personal offer

The first person to construct the requested square, or prove it impossible where the enigma permits, wins the listed cash prize and a bottle of champagne. The sponsor’s page says eight prizes remain, totaling €6,500; confirm submission logistics before relying on the offer.

Sponsor page remains online but its last recorded winner update is from 2017.

Award source ↗
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Sources & reading

1 unique reference linksSponsor’s remaining-enigmas page
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Related open targets

Recreational mathematicsBoyer enigma #1 · 3×3 magic square using at least seven squaresPPL 007 · €1,000 · 16 years openRecreational mathematicsBoyer enigma #3 · 3×3 semi-magic square of cubesPPL 009 · €1,000 · 16 years openRecreational mathematicsBoyer enigma #4 · 4×4 magic square of cubesPPL 010 · €1,000 · 16 years open