Question #575cd

1 Answer
George C.
Jun 10, 2017

#35#

Explanation:

Starting from #A#, 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)1#
#1color(white)(00)2color(white)(00)3color(white)(00)4color(white)(00)5color(white)(00)6#
#1color(white)(00000000)5#
#1color(white)(00000000)6color(white)(0)11color(white)(0)17#
#1color(white)(00000000)7color(white)(0)18color(white)(0)35#

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