All Puzzles

A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the five pirates: 1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics:

Infinitely smart.
Bloodthirsty.
Greedy.

Starting with pirate 5, they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if and only if a majority of the pirates agrees on it.

What proposal should pirate 5 make?

Four white pieces (the mice) are placed on one side of a chessboard, and one black piece (the cat) is placed at the opposite side. The game is played by the following rules:

black wins if it reaches the opposite side;
white wins if it blocks black in such a way that black cannot make any move anymore;
only diagonal moves (of length 1) on empty squares are allowed;
white only moves forward;
black can move backward and forward;
black may make the first move, then white makes a move, and so on.

Is this game computable (i.e. is it possible to decide beforehand who wins the game, no matter how hard his opponent tries to avoid this)?