MathDB

Alexandre and Bernado are playing the following game. At the beginning, there are

n

balls in a bag. At first turn, Alexandre can take one ball from the bag; at second turn, Bernado can take one or two balls from the bag, and so on. So they take turns and in

k

turn, they can take a number of balls from

1

k

. Wins the one who makes the bag empty.
For each value of

n

, find who has the winning strategy.

Problem Statement