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#

Related questions
See all questions in Pascal's Triangle and Binomial Expansion
Impact of this question
1260 views around the world
You can reuse this answer
Creative Commons License