The numbers 25 and 36 are written on a blackboard. At each turn, a player writes on the blackboard the (positive) difference between two numbers already on the blackboard, if this number does not already appear on the blackboard. The loser is the player who cannot write a number.
I tried but wasn't able to find any approach to this.
Original source appears to be: Mathematical Circles (Russian Experience), p.58page 58.