# Question

A total of 54 people were queuing to enter a concert hall. There were at least 3 men between any 2 women. What was the largest possible number of women in the queue?

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If you want the largest number of women, we shall put a woman to be the 1st person in the queue  and only 3 men (not more) in between. This will become a pattern recognition problem.

WMMM|WMMM|WMMM|WMMM……………………………………|WM

The pattern repeats in sets of 4 people. Where one set contain 1 woman and 3 men.

54/4 = 13 sets and remainder 2. The remainder 2 means the 14th set is incomplete with only 2 person, one woman and one man.

13 sets have 13 women and from the last incomplete set, we have one more woman.

Total women is 14# at max if we allow the 1st person in the queue to be a woman. ##