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Two persons Alex and Mac played a game of coins. In the game, a player can pick 1, 2 or 3 coins in his turn. If a person is left with 3 coins, he can choose to pick either 1, 2 or 3 coins and if a person is left with 2 coins, he can choose to pick either 1 or 2 coins. But if a person is left with only one coin, he will have to pick that coin. Assume that both the players play intelligently. Q.61 The option of picking 2 coins could not be exercised and the person who picked the last coin loses the game. If Alex started the game and won it, then which of the following could not be the number of total number of coins at the beginning of the game? a 20 b 30 c 25 d 48
Answer: c
In these kind of questions, the trick is start from 1 coin and take it forward. More often that not, there will be a pattern available. So, based on the number of coins, we can tell for sure which of the two players will win. Let me explain with the procedure.
If there is only one coin, the player who picks first (F) loses. So, the winner is the player who picks second (S).
If there are two coins, F can pick one coin. So, after F picks one coin, there is one coin left and S has to pick now. The situation is similar to the one above where the player who picks first loses. (in this case it is S who loses)
Similarly, if there are three coins, F can pick two coins and force S to lose.
Similarly, if there are four coins, F can pick three coins and force S to lose.
However, if there are five coins, irrespective of how many F picks, the ball is in S's court and he can force F to lose. Do you see that?
Expanding it further, whenever the number of coins is of the form 4k+1, the player who plays first loses. Every other time, the player who plays first wins. So, in the above options, the correct answer is c=25
Hello Maruti Sir, one doubt. In this question, the option of picking 2 coins could not be exercised. Then will the answer be same as well? Also can you please make a video on this? I have bought your course. It would be helpful for us.
