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What is the maximum number of bishops we can place on a \( 8 \times 8 \) chessboard so that none of the bishops can attack another in one move?

Note: A ...

Is it possible to write either a 0, a 1 or a 2 into each cell of a \(100\times 100\) square, such that the sum of the 100 numbers ...

\( f: \mathbb{R} \rightarrow \mathbb{R} \) is a function such that

\[ f(f(x)) = x^2 - x + 1 \]

What is the value of \(f(0) \)?

A heterosquare contains positive consecutive integers starting from 1 such that the rows, columns, and diagonals all add to different values. If the sums resulting from a heterosquare form a ...

\[\frac 1{3\times{0!}}+\frac 1{4\times{1!}}+\frac 1{5\times{2!}}+\frac 1{6\times{3!}}+\frac 1{7\times{4!}}+\cdots=?\]

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