2001 IMO Shortlist Problems/A1
Problem
Let denote the set of all ordered triples
of nonnegative integers. Find all functions
such that
![$f(p,q,r) = \begin{cases} 0 & \text{if} \; pqr = 0, \\ 1 + \tfrac{1}{6}\{f(p + 1,q - 1,r) + f(p - 1,q + 1,r) & \\ + f(p - 1,q,r + 1) + f(p + 1,q,r - 1) & \\ + f(p,q + 1,r - 1) + f(p,q - 1,r + 1)\} & \text{otherwise.} \end{cases}$](http://latex.artofproblemsolving.com/d/2/d/d2d4e8080418f5bb567971c0ee129fd02c7c7b13.png)
Solution
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