Einstein, the hyper-intelligent house cat, is busy walking from one corner of a rectangular room to the diagonally opposite corner in an apparently random manner. His rather stupid human slaves can’t work out what he is doing.
The light and dark carpet tiles on the floor look like part of a chess board, with exactly 10 tiles down the length and 6 tiles across the width. Einstein has decided to move from one corner of the room to the diagonally opposite corner, at each tile moving only down the length or across the width of the room.
How many different routes are there from one corner to the diagonally opposite corner?
[HINT: You could try an easier problem first.]
Author: Leslie Green