Excel in math, science, and engineering

8 identical small boxes and 4 identical chests, each capable of holding 2 of the boxes, are procured. In 4 of the small boxes, a golden cup is placed. In ...

Can you write all of \(\mathbb{R}^3\) (3-space) as the union of disjoint geometric circles? Give an example or prove that you can't.

(A geometric circle is a ...

Based on the success of our recent Problem Writing Parties, I have decided to hold a supplementary Wiki Writing Challenge that will not only show off our talented writers to ...

A peculiar functional equations question I found:

Find all functions \(f:\mathbb{Q} \rightarrow [-1,1]\) such that if \(xy=1\) or \(x+y\in\{0,1\}\) for distinct rational ...

1.Let \(\alpha\) and \(\beta\) be the two roots of the cubic polynomial \(x^3+ax^2+bx+c\) satisfying \(\alpha\beta+1 = 0\).Prove that ...

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