# If home is represented by blue house and store is red, how many possible routes can we take to get from house to store?

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Map of our town is represented in the map below:

If home is represented by the blue house and the store is represented by a red store, how many possible routes can we take to get from our house to the store?

posted Feb 26, 2017

For ease of calculation we can mark 2 points 1 and 2 at the top right and bottom right vertices respectively of the cube adjacent to home.

Starting from 1 effectively we have to move 3 steps to the right and 4 steps to the down assuming a rectangular grid.
So for a rectangular grid the number of paths from 1 to store is
(3+4)C(3) = 7C3 = 35. But since 3 vertices are missing 5 possibilities are removed, leaving us with 30 ways from 1 to store

Starting from 2 we have (3+3)C(3) = 6C3 = 20 ways for a rectangular grid. Since 3 vertices are missing again 5 possibilities are removed, leaving us with 15 ways from 2 to store.

Adding the 2 we get 30 + 15 = 45 ways to reach the store from house.

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