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What is the remainder of \(2009!\) divided by 2017?

Note: You should try solving it without using calculator. It's easy to write a program to solve this, but imagine ...

Let \(\sigma\) be a permutation of \(\{1, 2, 3, \ldots, 100\}\). Then there exists a smallest positive integer \(f(\sigma)\) such that \(\sigma^{f(\sigma)} = \text{id}\), where ...

You have an infinite stream of digits from 0-9, each digit produced uniformly at random. You want to produce a random integer in the following, unusual manner:

First, take the ...

You have a coin that comes out heads with probability \(p \in (0, 1)\). But you don't need it; you need to generate an event with probability ...

In the popular Pokémon franchise, there is a numbering of all the many species of Pokémon. For example, Bulbasaur has number 1, Pikachu has number 25, and Eevee has number ...

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