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Floor functions map a real number x to the largest integer less than or equal to x. You can probably guess what the ceiling function does.

What is \(\left\{\sqrt{71}\right\}\times\left(\sqrt{71}+8\right)?\)

**Note:** \(\{x\}\) denotes the fractional part function.

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by **Brilliant Staff**

What is \(\{21.11\}?\)

**Note:** \(\{x\}\) denotes the fractional part function.

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by **Brilliant Staff**

If \(0<x<50,\) how many solutions are there to \[\{x\}=0.9?\]

**Note:** \(\{x\}\) denotes the fractional part function.

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by **Brilliant Staff**

What is \(\{15.15\}+\{-15.15\}?\)

**Note:** \(\{x\}\) denotes the fractional part function.

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by **Brilliant Staff**

What is \(\left\{\frac{85}{6}\right\}?\)

**Note:** \(\{x\}\) denotes the fractional part function.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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by **Brilliant Staff**

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