Question #575cd

1 Answer
George C.
Jun 10, 2017

3535

Explanation:

Starting from AA, the number of paths to each junction is the sum of the number of paths to its immediate neighbours above and left.

Counting these, we find the following numbers at each junction:

1color(white)(00)1color(white)(00)1color(white)(00)1color(white)(00)1color(white)(00)11001001001001001
1color(white)(00)2color(white)(00)3color(white)(00)4color(white)(00)5color(white)(00)61002003004005006
1color(white)(00000000)51000000005
1color(white)(00000000)6color(white)(0)11color(white)(0)171000000006011017
1color(white)(00000000)7color(white)(0)18color(white)(0)351000000007018035

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