Floor and Ceiling (Hard)

Floor and Ceiling: core idea

• 1. How many integers $n$ satisfy $\lfloor n/3\rfloor=7$?

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• 2. Find $\lceil100/7\rceil$.

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• 3. Find $\sum_{k=1}^{10}\lfloor k/3\rfloor$.

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• 4. How many integers $n$ satisfy $0<\lfloor(n+2)/5\rfloor<4$?

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• 5. Find $\lfloor1/(\sqrt2-1)\rfloor$.

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• 6. Find greatest $n$ with $\lceil n/4\rceil=9$.

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• 7. How many nonnegative lattice points satisfy $x+y\le7$?

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• 8. Find $\lfloor999/13\rfloor+\lceil999/13\rceil$.

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• 9. Find $\lfloor\sqrt{50}+\sqrt8\rfloor$.

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