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It is known that a knight moves to a square that is two squares away horizontally and one square vertically, or two squares vertically and one square horizontally, which resembles ...

\[ \begin{array}{ccccc} & & & A & B\\ \times & & & & C\\ \hline & & A & 0 & B\\ \hline \end{array} \] Each of the letters ...

Consider all rational numbers that can be expressed as

\[\sqrt{\frac1a+\frac1b},\]

where \(a\) and \(b\) are coprime positive integers less than 1000.

The sum of all these numbers can ...

Let \(S\) denote a set of positive integers from \(1\) to \(k.\) Sort them

Imagine a list of all numbers from \(1\) to \(10^{100}\) arranged in alphabetical order. If all numbers smaller than \(10^{20}\) are removed from the list, what is the ...

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