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Recursive Equations : A 2x2xn hole in a wall is to be filled with 2n 1x1x2 bricks...

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Q.A 2x2xn hole in a wall is to be filled with 2n 1x1x2 bricks. In how many ways can this be done if the bricks are indistinguishable?

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Solution Summary

A recursive equation is used to find how many ways bricks can be placed in a hole in a wall. Diagrams are included with this well explained solution.

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let F(n) be the number of ways to fill the hole. Let's consider the following cases:
case 1: the first 2x2x1 part of the hole is filled by 2 bricks. There are two ways to fill this part with 2 bricks( either vertical or horizontal) and we have F(n-1) ways to fill ...

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