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Unbeatable Game

Updated on June 10, 2015

Who doesn't like winnings? Try this on your friends and leave them baffled in your awe. With any further delay, Let's start the game.

Rules:
1) There are a total of 35 sticks.
2) It is a 2 player game.
3) One player can pick a maximum of half the sticks that are left and a minimum of 1 stick.
For eg, If 35 sticks, at max you can pick at max 17 sticks and so on.
4) The player who picks the last stick loses.

Now, let's play one match between A and B.

1)A picks 12 sticks.
23 sticks remain.
2) B picks 5 sticks.
18 remains.
3) A picks 3 sticks.
15 remains.
4) B picks 7 sticks.
8 remains.
5)A picks 1 stick.
7 remains.
6) B picks 3 sticks.
4 remains.
7) A picks 1 stick.
3 Remains.
8) B picks 1 and then A picks 1,
Remaining 1 stick and B's turn. A wins.

Trick:
The trick is very simple. Always try to pick up number of sticks which results to remaining sticks as 4n-1.
ie. 1 less than multiple of 4 as in 3,7,11,15,19,23,27,31.
Look at the example now, every time after A's chance number of sticks remaining will be one of the above numbers.

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