Winning The Number Game!
What was the game?
Here the player whose number 'forces' sum to fall in range of 90-99 will be ending on losing side.
That means, somehow if you 'force' the total at some point to 89 then opponent has to fall in the range of 90-99 with his number.
To get 'door' to total 89 you have to force the previous sum to 78 so that opponent is forced to open a 'door' for total 89 for you.
And so on backward you have to make stops at 67, 56, 45, 34, 23, 12, 1.
So you have to start with 1 & achieve all above milestones.
Let's verify our conclusion. Suppose you started with 1.
You Sum Opponent Sum
1 - 8 9
3 12 5 17
6 23 7 30
4 34 9 43
2 45 4 49
7 56 10 66
1 67 3 70
8 78 2 80
9 89 4 93
7 100
YOU WIN!
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