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2001 Stanford Math Tournament Team #10

Source:

May 24, 2014
Stanfordcollegefunction

Problem Statement

You know that the binary function ⋄\diamond takes in two non-negative integers and has the following properties:
\begin{align*}0\diamond a&=1\\ a\diamond a&=0\end{align*} If a<b, then a⋄b&=(b−a)[(a−1)⋄(b−1)].\text{If } a<b, \text{ then } a\diamond b\&=(b-a)[(a-1)\diamond (b-1)].
Find a general formula for x⋄yx\diamond y, assuming that y\gex>0.
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