{"status": "success", "data": {"description_md": "A bag contains eight yellow marbles, seven red marbles, and five black marbles. Without looking in the bag, Igor removes $N$ marbles all at once. If he is to be sure that, no matter which choice of $N$ marbles he removes, there are at least four marbles of one colour and at least three marbles of another colour left in the bag, what is the maximum possible value of $N$?\n\n$\\text{(A)}\\ 6\\qquad\\text{(B)}\\ 7\\qquad\\text{(C)}\\ 8\\qquad\\text{(D)}\\ 9\\qquad\\text{(E)}\\ 10$\n\n___\n\n**[Pascal](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "

A bag contains eight yellow marbles, seven red marbles, and five black marbles. Without looking in the bag, Igor removes N marbles all at once. If he is to be sure that, no matter which choice of N marbles he removes, there are at least four marbles of one colour and at least three marbles of another colour left in the bag, what is the maximum possible value of N?

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\\text{(A)}\\ 6\\qquad\\text{(B)}\\ 7\\qquad\\text{(C)}\\ 8\\qquad\\text{(D)}\\ 9\\qquad\\text{(E)}\\ 10

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Pascal, by CEMC, is licensed under the CC BY-NC 3.0 DEED. They are not affiliated with or endorse TopsOJ in any way.

\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2006 Pascal Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/06_pascal_p25", "prev": "/problem/06_pascal_p23"}}