A total of 115 people stand in a queue for concert tickets. There are at least 3 men between any 2 women. What is the largest possible number of women in the queue? Ans: ___

1. Identify the repeating pattern to maximize the number of women

To maximize the number of women, we should place exactly 3 men between any 2 women, and start and end the queue with a woman. The pattern is: W, M, M, M, W, M, M, M, W, ...

2. Group the pattern and divide the total number of people

Consider a repeating group of 1 woman and 3 men (W, M, M, M). Each group has $1 + 3 = 4$ people.
Number of full groups in 115 people = $115 \div 4 = 28$ with a remainder of $3$.

3. Determine the number of women from the groups and remainder

In the 28 full groups, there are $28 \times 1 = 28$ women.
The remaining 3 people must follow the pattern, starting with a woman. So the remaining 3 people are W, M, M.
This adds 1 more woman.
Total number of women = $28 + 1 = 29$.