# Puzzle 63 | Paper ball and three friends

• Difficulty Level : Medium
• Last Updated : 11 May, 2017

It’s summer time and three of the college friends, A, B and C went to sports club to enjoy the vacation. They saw an interesting game being played there.

Game name is “hit and win”. There was a triangular setup of green ropes on ground. You have to move on the triangular path and on the turn you have to hit other mate using paper ball until only one is left for winning.

• A’s chances of hitting is 0.3.
• B has hitting chance of 0.5 .
• C has 100% chance of hitting the target.
• If a person is hit, he is out from path and cannot take a turn.
Suppose order of throwing balls is A, B, C. You being close to A, what strategy would you suggest A for having maximum chance of winning.

Solution: A has to miss the target first time purposely.

Explanation: Suppose if A tries to hit B and A is successful, then in the next turn C would definitely hit A and A looses.
If A tries to hit C and hits him, then B would go for A. Now if A purposely miss his target then B would go for C, he being more stronger than A. If he hits, its between A and B and A has a first chance to hit. If B misses the target, then C would go for B in next turn and he would definitely hit him and it would be now between A and C but again A has a first chance to hit.