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Here's one of my favorites. There are 99 bags, each of which contains some number of apples and some number of oranges. Prove that there's a way to select 50 out of the 99 bags, such that these 50 simultaneously contain more than at least half the total number of apples and more than at least half the total number of oranges. One fun aspect of this problem is that there are a number of distinct solutions, inspired by different areas of math. I know of at least three... |
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Here's one of my favorites. There are 99 bags, each of which contains some number of apples and some number of oranges. Prove that there's a way to select 50 out of the 99 bags, such that these 50 simultaneously contain more than half the total number of apples and more than half the total number of oranges. One fun aspect of this problem is that there are a number of distinct solutions, inspired by different areas of math. I know of at least three... |
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