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Maurice is 180 cm tall. When he stands on a bathroom scale, it reads 75 kg.

Now Maurice lies down on his back, supporting his body with a bathroom scale ...

Once again, a very large crowd of monkeys is sitting at typewriters with 26 letter keys.

Each monkey types a string of \(N\) letters at random. It turns out that ...

Let \(A \subset \mathbb Z\) be a non-trivial set of integers \((\)i.e. \(A \not= \emptyset\) and \(A \not= \mathbb Z).\) We call such a set \(A\) a "remarkable set ...

How many seven-digit positive numbers, containing no zeroes, are there such that the geometric mean of the first six digits is equal to the seventh digit?

In other words, how ...

The number 496 is the third smallest perfect number: the sum of its proper divisors is the number itself: \[1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 496.\]

But ...

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