Excel in math, science, and engineering

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Alice has a \(2\times 3\) chocolate bar. She wants to break it into 6 equal pieces by picking up every piece that is not size \(1\times 1\) (only ...

Today I learned that, for 2 positive integers \(a\) and \(b,\) \[\gcd(a,b)\times \text{lcm}(a,b)=a\times b.\] Can we extend this formula to 3 positive ...

For any positive integer \(n\), the following is true:

\(n\) is divisible by \(1.\) \(n(n+1)\) is divisible by \(1\times 2.\) \(n(n+1)(n+2)\) is divisible ...

Alice has 100 mL of apple juice, and Bob has 100 mL of orange juice.

Both of them want a mixture of apple and orange juice, so they come up ...

The only triangle with integer side lengths and a perimeter of 5 is the one in the diagram below.

How many triangles are there with integer side lengths and a ...

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