Question

Two players X and Y are playing a game of coins. Any player can pick 2, 3, 4, 5 or 6 coins in his turn. The player who picks the last coin always wins. If per chance their remains one coin for a person before his turn, then the game ends in a draw. While answering every question you will assume that each person is rational, intelligent and will always try to win the game. If Y starts the game and there are 32 coins, then what should he pick in order to ensure win, irrespective of whatever strategy X applies?
* He can never win
*6
*3
* 4​

Answer 1

Answer:

He can never win

Step-by-step explanation:

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Answer 2

Concept introduction:

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, if we are unclear of how an event will turn out. Statistics is the study of occurrences subject to probability.

Explanation:

Given that, Two players X and Y are playing a game of coins. Any player can pick $2, 3, 4, 5$ or $6$ coins in his turn. The player who picks the last coin always wins. If per chance their remains one coin for a person before his turn, then the game ends in a draw.

We have to find, If Y starts the game and there are $32$ coins, then what should he pick in order to ensure win, irrespective of whatever strategy X applies.

According to the question,

If X picks $4$ coins, there are $7$ coins left on the table. The table shows all the possible cases, and it can be seen that Y loses in all of these cases.

X Y X Y

$4 5 1 1$

$4 4 2 1$

$4 3 3 1$

$4 2 4 1$

$4 1 5 1$

If X picks $5$ coins, then X will loose if Y picks $5$ coins, as there will be only one coin left.

If X picks $2$ or $3$ coins, then X will loose if Y picks $1$ coin.

Similarly, we can check all the cases and $4$ will be the only possible answer.

Final Answer:

$4$ will be the only possible answer.

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