I submitted this problem, but it was rejected since it does not fit well into any of the categories [EDIT: or not] (I personally thought it could fit into Combinatorics, what do you think?).

There are 15 marbles in a bag, in exactly 5 different colors. Grabbing marbles randomly without replacement, it takes at most 9 grabs to get three marbles of the same color, and at most 14 grabs to get five marbles of the same color.

Find the sum of the maximum number of grabs it takes to get four of a color in each of the possible arrangements that satisfy the above conditions.

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## Comments

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TopNewestThe problem was mainly rejected because your phrasing was unclear. What are the different scenarios that we should consider? If the marbles are distributed as \( \{ 1, 2, 3, 4, 5\} \), should it be considered different from \( \{5, 4, 3, 2, 1 \} \)? Do you want sum of distinct maximum number, or sum of maximum number for each distinct configuration (after dealing with the definition of distinct).

Note that the version which you submitted had a different question, involving the "sum of possible products", which made it even more confusing.

On the whole, I do like the ideas involved in this question.

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Yes, I do understand that. I had trouble with some of the phrasing, and especially the question. A conventional question statement wouldn't really fit.

I don't suppose that I could submit it again with some fixes, since I already posted it (I could delete it :) ). Oh well.

Thanks for the feedback!

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Can anyone solve this? I will post the solution eventually. I want to know how hard it is :)

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