MathDB

Shakur and Tiham are playing a game. Initially, Shakur picks a positive integer not greater than

1000

. Then Tiham picks a positive integer strictly smaller than that.Then they keep on doing this taking turns to pick progressively smaller and smaller positive integers until some one picks

1

. After that, all the numbers that have been picked so far are added up. The person picking the number

1

wins if and only if this sum is a perfect square. Otherwise, the other player wins. What is the sum of all possible values of

n

such that if Shakur starts with the number

n

, he has a winning strategy?

Problem Statement