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\(f(x, y)\) is defined as a random natural number between \(x\) and \(y\) inclusive. For example, \(f(1, 3)\) would be a random natural number of either 1, 2 ...

There are 100 people on an island; some people always tell the truth, and the others always lie.

A visitor asks them, "How many of you tell the truth?"

For ...

\[\large \int_{0}^{1} 5^{\ln(x)} dx =?\]

A blind-folded magician gave 10 balls, marked with the digits 0 to 9 distinctly, to the five volunteers and told each of them to make up 2-digit numbers from the ...

Nine distinct light bulbs are placed in a circle, each of which is off. Then the number of ways to turn on some of the light bulbs in the circle ...

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