Planned The Unbeatable Strategy!
What is the game?
The first person can plan an unbeatable winning strategy.
CASE 1 : The person picking last stick is winner.
All that he has to do is pick 4 sticks straightaway at the start leaving behind 96 stick. Then, he has to make sure that the count of remaining stick will be always divisible by 6 like 96, 90, 84, 78......6.
So if the opponent takes away 2 sticks in his first turn, then first person has to take 6 - 2 = 4 sticks leaving behind 90 sticks there. That is if the opponent takes away X stick the first person need to pick 6 - X sticks.
Now, when there are 6 stick left, even if opponent takes away 5 sticks then 1 stick will be left for the first person.
And even if the opponent picks 4 sticks then first person will take 2 remaining sticks.
CASE 2 : The person picking last stick is looser.
Now the first person need to take away 3 sticks in first turn leaving behind 97. Next, he has to make sure the count of remaining sticks reduced by 6 after each of his turn. That is, the count should be like 91,85,79,72......7.
So if the opponent takes away 4 sticks in his first turn, then first person has to take 6 - 4 = 2 sticks leaving behind 91 sticks there. That is if the opponent takes away X stick the first person need to pick 6 - X sticks.
When there are 7 sticks are left then even if the opponent takes away 5 sticks then first person can force him to pick the last stick by picking only 1 stick of remaining 2.
And if the opponent takes away 4 sticks at this stage, the first person still can force him to pick last stick by picking 2 of remaining 3 sticks.
Conclusion : The first person always has a chance to plan a winning strategy.
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