MathDB

The numbers

1,2,3,\dots,1000

are written on the board. Patya and Vassya are playing a game. They take turn alternatively erasing a number from the board. Patya begins. If after a turn all numbers (maybe one) on the board be divisible by a natural number greater than

1

the player who last played loses. If after some number of steps the only remaining number on the board be

1

then they call it a draw. Determine the result of the game if they both play their best.

Problem Statement