Instructions

based on the following information.

From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.

Question 81

Which position should a contender choose if he has to be the leader?

Solution

If the group had two members, the one in the first position would win.

If the group had three members, the one in the third position would win.

If the group had four members, the one in the first position would again win.

Similarly, for five members, the one in the third position will win

Similarly, for six members, the one in the fifth position will win.

So, for f(2n), the one at 2f(n)-1 will win

And for f(2n+1) members, the one at 2f(n)+1 will win.

When 2n = 2, the winner will be 1.

For 2n = 4, winner will be 2f(2) - 1. And since f(2)=1, for f(4), the winner will be 1.

Now, f(545) = 2f(242) + 1

f(272) = 2f(136) - 1

f(136) = 2f(68) - 1

f(68) = 2f(34) - 1

f(34) = 2f(17) - 1

f(17) = 2f(8) + 1

f(8) = 2f(4) - 1

f(4) = 2f(2) - 1

Since f(2) = 1, f(4) = 1,f(8) = 1,.......f(545) = 67

Thus, the correct option is B.

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