PROBLEM OF THE MONTH
FEBRUARY 2002
There are several possible solutions to this problem including a ... "brute force" approach of writing computer code that would enumerate and test all possible scenarios!
Here is one way to model and solve the problem:
The are altogether small cubes of size and one may divide them in two groups:
Observe now that each time the mouse eats an allowed small cube of cheese, it
has to pass from a cube in the first group to one in the second group
or vice-versa. On the other hand the center cube belongs to the second group
(of only small cubes). So if there would be a way such that the mouse could eat
the center small cube on the last day, then it should have eaten
a small cube belonging to the second group also on days
,
which is impossible since the are only cubes in that group.