Problem 380

Amazing Mazes!

An mn maze is an mn
rectangular grid with walls placed between grid cells such that there
is exactly one path from the top-left square to any other square.

The following are examples of a 912 maze and a 1520 maze:

Let C(m,n) be the number of distinct mn mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.

It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415, and
C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant
digits).

Find C(100,500) and write your answer in scientific notation rounded to 5 significant digits.

When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 1234567891011 then the answer format would be 1.2346e12.

**
These problems are part of
Project Euler
and are licensed under
CC BY-NC-SA 2.0 UK
**