MathDB

In the middle cell of the

1 \times 2005

strip there is a chip. Two players each queues move it: first, the first player moves the piece one cell in any direction, then the second one moves it

2

cells, the

1

st - by

4

cells, the 2nd by

8

, etc. (the

k

-th shift occurs by

2^{k-1}

cells). That, whoever cannot make another move loses. Who can win regardless of the opponent's play?

Problem Statement