Problems

By considering \(k-1\) copies of \(K_{k-1}\), show that \(R(k,k)\ge(k-1)^2\).

Let \(s>2\) and \(t>2\) be integers. Show that \(R(s,t)\le R(s-1,t)+R(s,t-1)\).

Using \(R(s,t)\le R(s-1,t)+R(s,t-1)\), prove that \(R(k,k)\le 4^k\).

Show that \(R(k,k)\ge2^{k/2}\).

Explain why you can’t rotate the sides on a normal Rubik’s cube to get to the following picture (with no removing stickers, painting, or other cheating allowed).