Problem 629

[tamandua]

Got stuck with understanding the specification :
Why is f(5,2) = 3 ?
k=2 means that there are only 2 piles allowed, so IMHO only {2,3} and {1,4} are allowed. So why is there {1,1,1,2} in the list ?
And why is f(5,3) = 5 ? Why is {5} in the list which does not look similar to a split as required ?

[Animus]

hi, tamandua

The parameter $k$ does not restrict the number of piles in the starting position nor the number of piles present after a valid move, only the number of piles a single pile may be split into. Therefore is {1,1,1,2} a valid starting position for a game with $k=2$, and happens to be a winning position (since Alice can split the pile of two into two piles of one and Bob is left without possible moves).
The same applies to the starting position {5} in $f(5,3)$.

Hope this helps clarifying.

[tamandua]

THX, now I see. The magic word is "total number of stones".