Here is a two player game – there are three piles of stones: one with 10 stones, one with 15 stones, and one with 20 stones. At each turn, a player can choose one of the piles and divide it into two smaller piles. The loser is the one who cannot do this. Who will win and how?
Source: Mathematical Circles, by Dmitri Fomin, Sergey Genkin and Ilia Itenberg
Age Group: For all ages
Note: please mail answers to alokgoyal_2001@yahoo.com
Alok Goyal's Puzzles Page 
Total moves possible is 10+15+20-1 = 44 As 44 is even number, so whoever will start the game will lose