The following question came up at a conference and a solution took a while to find. Puzzle. Find a way of cutting a pizza into finitely many congruent pieces such that at least one piece of pizza ...
Find 2 tetrahedrons $ABCD$ and $EFGH$ such that $EFGH$ lies completely inside $ABCD$. The sum of edge lengths of $EFGH$ is strictly greater than the sum of edge lengths of $ABCD$. I am completely ...
I found this puzzle here. (It's labeled "crossed cylinders".) Here's the description: Two cylinders of equal radius are intersected at right angles as shown at left. Find the volume of the ...
I remember being presented a mathematical puzzle some years back that I still can't solve. The problem is defined as follows: We have two points on a plane, and using only a compass, how do we find ...
A sailor gets some treasure and wants to hide it. He finds an island where there are two poles $P_1$ and $P_2$ and a tree $T$. He goes from $P_1$ to $T$ and turns right angle anti-clockwise and ...
Given a line segment $AB$ and a point $P$ inside a circle, can one construct a chord through $P$ congruent to $AB$?
This is a little exercise found in Robin Hartshorne's Euclid: Geometry and Beyond: I believe I have found a solution, which only exists when $AB$ has length at least that of the chord bisected by ...