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Question
In the diagram below, how many distinct paths are there from the start to the finish, moving from one adjacent dot to the next either to the right, down, or diagonally down to the right?
In the diagram below, how many distinct paths are there from the start to the finish, moving from one adjacent dot to the next either to the right, down, or diagonally down to the right?
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Solution
The correct option is B 372
For each dot in the diagram, we can count the number of paths from the start to it by adding the number of ways to get to the dots to the left of it, above it, and above and to the left of it, starting from the topmost leftmost dot (using a simple logic that the value of each dot is the sum of the values of the incoming dots).
This yields the following numbers of paths: 
372
For each dot in the diagram, we can count the number of paths from the start to it by adding the number of ways to get to the dots to the left of it, above it, and above and to the left of it, starting from the topmost leftmost dot (using a simple logic that the value of each dot is the sum of the values of the incoming dots).
This yields the following numbers of paths:
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