One of the contending politicians, Mr. Chanaya, was quite proficient in calculations and could correctly figure out the exact position. He was the last person remaining in the circle. Sensing foul play the politicians decided to repeat the game. However, this time, instead of removing every alternate person, they agreed on removing every 300th person from the circle. All other rules were kept intact. Mr. Chanaya did some quick calculations and found that for a group of 542 people the right position to become a leader would be 437. What is the right position for the whole group of 545 as per the modified rule?
Explanation:
Let f (n, k) represent the position of a winner when there are n people out of which every kth person is eliminated.
We have,
f (n, k) = (f (n – 1, k) + k)mod n
Now f (542, 300) = 437
Hence,
f (543, 300) = (437 + 300) mod 543 = 194
f (544, 300) = (194 + 300) mod 544 = 494
f (545, 300) = (494 + 300) mod 545 = 249
∴ A contender at 249th position will win the election.
Hence, option (c).
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