Magic square of squares

Importance: Medium ✭✭
Author(s): LaBar, Martin
Keywords:
Recomm. for undergrads: yes
Prize: $100 + €1,000 + a bottle of champagne
Posted by: maxal
on: November 23rd, 2008

\begin{question} Does there exist a $3\times 3$ \Def{magic square} composed of distinct perfect squares? \end{question}

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 \cite{Bc}. For a review of the history of research, see \cite{Ba, Bb, Bc}. For basic facts about the anticipated $3\times 3$ magic square of squares, see \cite{Br, Mo}.

Bibliography

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

[Bb] Christian Boyer. \href[Magic squares of squares]{http://multimagie.com/English/SquaresOfSquares.htm}, "Multimagic Squares" website.

[Bc] Christian Boyer. \href[Latest research on the "3x3 magic square of squares" problem]{http://multimagie.com/English/SquaresOfSquaresSearch.htm}, "Multimagic Squares" website.

[Br] Kevin Brown. \href[Magic Square of Squares]{http://www.mathpages.com/HOME/kmath417.htm}, "Math Pages" website.

[Mo] Lee Morgenstern. \href[3x3 Magic Square of Squares Formulations]{http://home.earthlink.net/~morgenstern/magic/sq3.htm}


* indicates original appearance(s) of problem.