🚀 go-pugleaf

From article <9105242046.AA15308@athos.cs.ua.edu>, by borie@ATHOS.CS.UA.EDU (Richard Borie):
> Is it possible to partition the interior of a square into
> smaller squares, no two of which have the same size?

Indeed it is.  I found the following in Martin Gardner's "Mathematical
Diversions":

	The best known problem of this type is that of fitting a
	set of squares no two of which are alike into a larger
	square without any overlap or leftover space.  If we think
	of the larger square as a lattice of unit squares to be
	divided along lattice lines into unequal squares, the
	smallest-known square that can be so divided has a side of
	175 units.  It can be cut into 24 unequal squares.  The
	reader will find a picture of it on page 206 of "The 2nd
	Scientific American Book of Mathematical Puzzles &
	Diversions", in a chapter by William T. Tutte explaining
	how he and his friends used electrical-network theory to
	find "squared squares" of this type.

In case it sounds like this contradicts Neil Calkin's posting I should
reiterate someone else's posting:  the 112x112 square is the smallest
decomposable square when 'smallest' is measured in terms of the number of
pieces required, the 175x175 square is the smallest known when 'smallest'
is measured in terms of the length of the sides of the square.
--
 "Merely corrobarative detail, intended to give artistic verisimilitude
 to an otherwise bald and unconvincing narrative"    -- W.S. Gilbert 

Name: Michael Chisnall		email: chisnall@cosc.canterbury.ac.nz