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On a chessboard of a finite size, we want to place kings and knights such that each king attacks exactly 2 kings and 2 knights, and each knight attacks exactly ...

\[1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 = 3^3 + 4^3 = 91.\]

Are there any other (non-trivial) sets of consecutive squares and cubes whose sums ...

Let \(x_1,x_2,\cdots,x_{19},x_{20}\) be permutations of numbers from 1 to 20. Then what will be the maximum value of the summation ...

Hi, I have an interesting question posed by my University Mathematics Professor.

It is by definition that the Lagrangian method: L(x,y) = f(x,y) - λ * [g(x,y ...

If I win when I flip more consecutive heads than I've ever flipped tails, what's my probability of winning?

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