U N S O L V E D :

Is there a square with integer side lengths and a point in the plane whose distance to each corner of the square is an integer?

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Does an odd perfect number exist?

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Find a method to determine whether or not any given knot is invertible.

What is the best way to cut a donut up into tetrahedra?

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Can you cut a rectangle into 3 congruent non-rectangular pieces?

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Pick a positive whole number n; if odd, replace with 3n+1, if even divide by 2, repeat ...

Are there infinitely many even perfect numbers?

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Is there a single aperiodic tile?

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