PPL 013 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.27
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Prize Problem LedgerBoyer magic-square enigmasPPL 013Boyer enigma #6 · 5×5 additive–multiplicative magic square

Permanent problem IDPPL 013

Reconfirm sponsorIndependentexistence

Recreational mathematics

Boyer enigma #6 · 5×5 additive–multiplicative magic square

Construct, or prove impossible, a 5×5 square of distinct positive integers whose rows, columns and main diagonals have both equal sums and equal products.

magic squaresDiophantine equationsconstruction
01

The problem

Construct, or prove impossible, a 5×5 square of distinct positive integers whose rows, columns and main diagonals have both equal sums and equal products.

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 ↗
03

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 #2 · 5×5 bimagic square with distinct positive integersPPL 008 · €1,000 · 16 years openRecreational mathematicsBoyer enigma #3 · 3×3 semi-magic square of cubesPPL 009 · €1,000 · 16 years open