perplexus.info :: Shapes : Counting the Tilings

Counting the Tilings (Posted on 2023-08-29)

A rectangle has dimensions of 3 by 30. How many ways can this rectangle be tiled with 1 by 2 dominoes?
The dominoes can go in either orientation. A rotation or reflection of an asymmetric solution is considered distinct.

Provide a formula for a generalized 3 by 2n rectangle.

A classic version of this puzzle is for a 2 by n rectangle.

See The Solution Submitted by Brian Smith

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re: Solution

Comment 2 of 2 |

(In reply to Solution by Jer)

Bravo! Jer. I had messed up this one.

Later I found this URL, which agrees with your analysis and has some programs to compute the values:

https://www.geeksforgeeks.org/tiling-with-dominoes/

Posted by Charlie on 2023-08-29 13:28:47

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