Magic square of squares

Importance: Medium ✭✭
Author(s): LaBar, Martin
Recomm. for undergrads: yes
Prize: $100 + €1,000 + a bottle of champagne
Posted by: maxal
on: November 23rd, 2008
Question   Does there exist a $ 3\times 3 $ magic square composed of distinct perfect squares?

This question was first asked in 1984 by Martin LaBar and popularized in 1996 by Martin Gardner, who offered $100 to the first person to construct such a square. In 2005 Christian Boyer offered €1,000 and a bottle of champagne for a solution to a somewhat easier problem [Bc]. For a review of the history of research, see [Ba, Bb, Bc]. For basic facts about the anticipated $ 3\times 3 $ magic square of squares, see [Br, Mo].


[Ba] Christian Boyer. Some notes on the magic squares of squares problem. The Mathematical Intelligencer 27 (2005), 2, 52-64.

[Bb] Christian Boyer. Magic squares of squares, "Multimagic Squares" website.

[Bc] Christian Boyer. Latest research on the "3x3 magic square of squares" problem, "Multimagic Squares" website.

[Br] Kevin Brown. Magic Square of Squares, "Math Pages" website.

[Mo] Lee Morgenstern. 3x3 Magic Square of Squares Formulations

* indicates original appearance(s) of problem.