The numbers 1,2,…,2000 are written on the board. Two players are playing a game with alternating moves. A move consists of erasing two number a,b and writing ab. After some time only one number is left. The first player wins, if the numbers last digit is 2, 7 or 8. If not, the second player wins. Who has a winning strategy?[I]Proposed by V. Frank combinatoricsInvariantsgames