Taxi route counts #2

d = 1 d=1 and V = ( 1 , 1 ) \vec{V}=(1,1) .

There are a positive integer number, d d , of independent vectors, V i \vec{V}_i , where i i runs from 1 to d d . A trip starts from the appropriate 0 \vec{0} of d d components and goes to a destination vector of d d positive integer components. A step of a trip consists of adding 1 1 to a single component of the taxi's current position vector which was initially 0 \vec{0} of d d components. How many distinct routes would accomplish this trip?


The answer is 2.

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1 solution

The first step increments either the first or second coordinate of the position vector. The second step is forced. Therefore, the answer is 2.

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