Difference between revisions of "2006 Canadian MO Problems/Problem 1"
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Let <math>f(n,k)</math> be the number of ways distributing <math>k</math> candies to <math>n</math> children so that each child receives at most two candies. For example, <math>f(3,7)=0</math>, <math>f(3,6)=1</math>, and <math>f(3,4)=6</math>. Evaluate <math>f(2006,1)+f(2006,4)+f(2006,7)+\dots+f(2006,1003)</math>. | Let <math>f(n,k)</math> be the number of ways distributing <math>k</math> candies to <math>n</math> children so that each child receives at most two candies. For example, <math>f(3,7)=0</math>, <math>f(3,6)=1</math>, and <math>f(3,4)=6</math>. Evaluate <math>f(2006,1)+f(2006,4)+f(2006,7)+\dots+f(2006,1003)</math>. | ||
==Solution== | ==Solution== | ||
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{{solution}} | {{solution}} | ||
| + | ==See also== | ||
*[[2006 Canadian MO]] | *[[2006 Canadian MO]] | ||
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| + | {{CanadaMO box|year=2006|before=First question|num-a=2}} | ||
Revision as of 18:56, 7 February 2007
Problem
Let 
be the number of ways distributing 
candies to 
children so that each child receives at most two candies. For example, 
, 
, and 
. Evaluate 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2006 Canadian MO (Problems) | ||
| Preceded by First question |
1 • 2 • 3 • 4 • 5 | Followed by Problem 2 |
