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Recreational mathematics or puzzles with serious mathematical content. Note that math contest problems are generally considered off-topic.

5 votes
Accepted

Wrapping a suitcase with large rotational symmetry

Edit: my previous answer was incorrect No, this one you cannot do. If one had such an arrangement of circles in the solid torus inside $R^3$, and quotiented by a rotation, then by the equivariant Dehn …
Ian Agol's user avatar
  • 68.9k
11 votes

Can I wrap a suitcase with hair ties

I shared this question with Michael Freedman who came up with a solution similar to Larsen’s and asked me to post on his behalf. He made a physical realization too. I’ll address Anton’s question of …
6 votes

Math puzzles for dinner

Suppose 100 ants are placed randomly (with random orientations) along a yard stick. Each ant walks at a pace of an inch a minute. Each time two ants meet, they instantaneously reverse direction, and i …
34 votes

Is it possible to capture a sphere in a knot?

I would try to "gift wrap" the sphere. Take the 1-skeleton of the octahedron, and take an Eulerian path. Then make each vertex into a twist, and pull tight, so that it looks like the union of three o …
Ian Agol's user avatar
  • 68.9k