Here's a puzzle I pondered earlier today and eventually solved. Does there exist a cycle (self-avoiding cyclic walk) in Z^3 such that: (a) The three projections on to the xy, yz and zx planes are trees; (b) The cycle has order-3 rotational symmetry; (c) The cycle is a trefoil knot? Satisfying properties (b) and (c) is very easy, whereas satisfying (a) (even on its own, without (b) and (c)) is rather difficult (try it). Amazingly, it is possible for a cycle to satisfy all three properties simultaneously: http://cp4space.wordpress.com/2012/12/12/treefoil/ Can you find a smaller solution than 11 x 11 x 11? I know for certain that there isn't one in a 3 x 3 x 3 box. Sincerely, Adam P. Goucher