>In van Lint & Wilson's "A Course in Combinatorics", page 460, they make the
>following citations at the end of their chapter "Electrical networks and
>squared squares:
>
>W.T. Tutte (1961), Squaring the Square, in: M. Gardner, "The 2nd Scientific
>American Book of Matheamtical Puzzles and Diversions", Simon and Schuster.
>
>W.T. Tutte (1965), The quest of the perfect square, Amer. Math. Monthly 72, No.
>2, 29-35.
>
>
>Sam, I would guess that Scientific American is the original source, but I can't
>check.
Well... Ed, let me check it (at least this one is not misplaced... :-):
The article "Squaring the Square" included in MG's 2nd collection is wriiten
by W. T. Tutte. Here is MG's preface (p. 186):
Can a square be subdivided into smaller squares of which no two are alike?
This enorously difficult problem was long thought to be unsolvable, but now
it has been defeated by translating it into electrical-network theory, then
back into plane geometry again. Here William T. Tutte, associate professor of
mathematics at the University of Toronto, presents a fascinating account of
how he and three fellow students at the University of cambridge finally
squared the square.
> The van Lint & Wilson chapter on squared squares is quite entertaining
>and informative in its own right. It makes the suggestion that squared squares
>even have practical applications! I recommend the book.
>
> Ed Sandifer
>
>--------------
>
>Samuel S. Kutler wrote:
>
>>The smallest squared square consists of a square disected into 21 squares
>>all different.. It was to my amazement that there can be no cubed cube. I
>>know the proof of Tutte, which is very beautiful. But where and when did
>>he publish it?
The book contains an addendum by MG, where we read (p. 208):
Is it possible to dissect a cube into a finite number of smaller cubes, all
different sizes?
No, and a beautiful proof of this is given by "Important Members" in the
fourth entry in the list of references. The proof runs as follows:
[...]
Let's now go to the list of references. The 4th entry reads:
"The Dissection of Rectangles into Squares." R. L. Brooks, C. A. B. Smith,
A. H. Stone and W. T. Tutte in Duke Mathematical Journal, Vol. 7, pages
312 - 340, 1940
Antreas