Talk:2011 AIME I Problems/Problem 12

I think in the solution of this problem some cases are repeated and correct answer

denominator: n+3

Solution is incorrect

I don't see where $\dbinom{n+3}{3}$ or $\dbinom{n+2}{2}$ came from. I'm getting $\dbinom{n+1}{3}$ and $\dbinom{n+1}{2}$, respectively. Case 2 is identical to cases 3 and 4. In case 1, the number of women is still the same, only that we are adding more dividers. The number of possible dividers that could potentially be added is the same.

Update: I rewrote the solution. Check to see if it is correct. It's really long, so there may be a much better solution.


If you actually solve the inequality at the end by hand with the quad. formula, you get 593 as the answer.

I rewrote the solution; I believe the error is corrected - hesa57