Difference between revisions of "2001 IMO Shortlist Problems/A1"
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==Problem== | ==Problem== | ||
| − | {{ | + | Let <math>T</math> denote the set of all ordered triples <math>(p,q,r)</math> of nonnegative integers. Find all functions <math>f:T \rightarrow \mathbb{R}</math> such that |
| + | <center><math>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}</math></center> | ||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == Resources == | ||
| + | |||
| + | * [[2001 IMO Shortlist Problems]] | ||
| + | * [http://www.artofproblemsolving.com/Forum/viewtopic.php?t=17447 Discussion on AOPS/MathLinks] | ||
| + | |||
| + | [[Category:Olympiad Algebra Problems]] | ||
Revision as of 18:26, 20 August 2008
Problem
Let 
denote the set of all ordered triples 
of nonnegative integers. Find all functions 
such that
Solution
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