MathDB

1

Part of 2006 Canada National Olympiad

Problems(1)

number of ways of distributing $k$ candies to $n$ children

Source: Canadian Mathematical Olympiad 2006 , problem 1

1/28/2007
Let f(n,k) f(n,k) be the number of ways of distributing k k candies to n n children so that each child receives at most 2 2 candies. For example f(3,7) \equal{} 0,f(3,6) \equal{} 1,f(3,4) \equal{} 6. Determine the value of f(2006,1) \plus{} f(2006,4) \plus{} \ldots \plus{} f(2006,1000) \plus{} f(2006,1003) \plus{} \ldots \plus{} f(2006,4012).
combinatorics proposedcombinatorics