2 problems

Fix an arbitrary order on the positions of the corners of a Rubik's cube. Let $X_t$ denote the configuration of the cube at time $t$, and call two corners unlinked when they are un…

Let $M$ be an oriented map with vertex set $V(M)$ and edge set $E(M)$, and let $H_1(M)$, $H_2(M)$, and $H_3(M)$ be the kernels of the successive homomorphisms in the decomposition…