A rectangle ABCD is to be cut into three pieces
(with two straight line cuts) and the pieces re-
arranged into a square.

Define the endpoints of the cuts.

Note 1: |AB|/4 ≤ |BC| < |AB|.

Note 2: A straight line cut (as the name implies)
            is a cut along a straight line that
            divides a piece into two pieces.

(In reply to re(2): Full solution by Bractals)

yes, I just noticed my mistake.  Jer's solution only works if the horizontal cut intersects with the diagonal cut.  Thus we need y<=x which gives
n-sqrt(mn)<=sqrt(mn)
n<=2*sqrt(mn)
n^2<=4mn
n/4<=m<=n
which fits the restriction in note 1.

Posted by Daniel on 2013-08-16 14:50:13