Poornimayashas wrote:
I still didn't understand. This is not a probability question to guess how many they will pick at a time. It's 1,2,3, 4 or 5. Confusing!
Posted from my mobile device
Hi - This is a reasoning question.
Question: Rita and Sam play the following game with n sticks on a table. Each must remove 1, 2, 3, 4 or 5 sticks at a time on alternate turns, and no stick that is removed is put back on the table. The one who removes the last stick (or sticks) from the table wins. If Rita goes first, which of the following is a value of n such that Sam can always win no matter how Rita plays?
Explanation: Let us first decide the winning strategy for Rita:
In order to win, Rita (R) must be able to pick the last stick.
In order to decide the winning strategy, Rita must be able to make something constant in the game based on which he would do her calculations.
For any number of sticks that Sam picks, say k, Rita can always pick (6 – k) sticks in her next pick; thus maintaining the sum of the number of sticks as {k + (6 – k)} = 6, i.e. a constant.
For example: If Sam picks 1, Rita can pick 6 – 1 = 5; if Sam picks 2, Rita can pick 6 – 2 = 4; and so on ... if Sam picks 5, Rita can pick 6 – 5 = 1.
Thus, if the number of sticks is 52 (let us assume any random number to see what happens), we would have: We remove as many multiples of 6 as possible from 52, we would be left with 4 sticks. Rita needs to pick all 4 of these in the beginning so that she can finish the game. The sequence in which the sticks are picked would have been:
Attachment:
11.JPG [ 17.5 KiB | Viewed 37818 times ]
Now, let us decide: how can Rita lose? This can only happen if the total number of sticks is a multiple of 6. In that case, Rita HAS to pick some number in the first draw; and then, Sam will use the above strategy and ensure Rita loses. The diagram below explains this situation:
Let the number of sticks be 24 (a multiple of 6) and Rita picks k in the first attempt:
Attachment:
111.JPG [ 13.88 KiB | Viewed 37761 times ]
The only multiple of 6 in the options is 12
Answer D