This problem was first put to me by Luke Pebody (who did not know the answer at the time) and after some work I am yet to find a proof or counterexample. I would be grateful of any …

Given a pizza, represented by the unit disk $D_1(0,0)=\{(x,y)\in\mathbb{R}^2\mid \|(x,y)\|\leqslant 1\}$, and given $N$ slices of $r$-pepperoni, represented by disks $D_r(a_i,b_i)= …

In this recent question http://mathoverflow.net/questions/29323/math-puzzles-for-dinner/29343#29343 we had a nice time as we were asked to provide new maths puzzles for dinners. I …