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To ensure that any 90 guests can access the 90 rooms, we can use a combinatorial design approach. Assign each room a unique key and distribute keys in such a way that each guest receives keys to 90 out of the total 100 rooms. Specifically, for each guest, we can select their keys from a combination of the available rooms, ensuring that no matter which 90 guests are present, they can always find a key to each of the 90 rooms, thereby ensuring coverage. This can be accomplished by carefully organizing the key distribution to guarantee that all combinations are accounted for.

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1w ago

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