22 Apr
2003
22 Apr
'03
11:48 a.m.
On Tue, Apr 22, 2003 at 11:33:57AM -0400, Michael Kleber wrote:
... Theorem: Suppose you tile an axb rectangle with 1xn (and nx1) strips, and suppose a,b are no smaller than n. Then there must be an nxn square tiled with n aligned horizontal or vertical strips. ... Step 2: Further define a "valley of length k", the arrangement
A B A B A111222333...kkkB
Claim: a valley of length k must contain a valley of length j for some j<k.
Pf: ...
So by induction, we're done.
Why does there have to be a valley at all? Peace, Dylan