Hint for Puzzle #10: Number Game Call Out 50

10. You and I are to play a competitive game. We shall take it in turns to call out integers. The first person to call out '50' wins. The rules are as follows:
–The player who starts must call out an integer between 1 and 10, inclusive;
–A new number called out must exceed the most recent number called by at least one and by no more than 10.

Do you want to go first, and if so, what is your strategy?
smile faces for the number game puzzle

The player will win if he shouts out 50. We need to think under what circumstances within the rules of the game will allow him to shout out 50, as in what numbers being called out by the opponent will permit this. How he can force his opponent into that position.... and work backwards to the beginning to find out how the game must start for our player to win.


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