Notice that now there are 7 sons left. Four must agree for the second son to get his way, otherwise he gets nothing, and the third son gets a crack at splitting the money. This process continues until a majority agrees. No son trusts any other son. A son will agree with a distribution if he knows that he can't expect to get any more.
All sons act with reason.
Some bi-chrome plane problems Assume that every point in the plane is colored either red or blue. Show that the subset has non-empty interior. The ant is located 1 foot from the ceiling and five feet from both sides of the wall. The food is symmetrically located 1 foot from the floor and five feet from the sides of the wall.