2001 IMO Shortlist Problems/A1: Difference between revisions
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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 17:26, 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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