Problem 58946. Count block fountains

Created by ChrisR

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A block fountain consists of rows of circles in which each row is a continuous block of circles (i.e., adjacent circles are tangent) and each circle in a row above the first touches exactly two circles on the previous row. 
Write a function to compute the number of block fountains with n circles on the first row. For example, there are five block fountains with three circles on the first row. 

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17 Solutions
8 Solvers

Last Solution submitted on Jan 26, 2026

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3 Comments

3 Comments

William on 3 Sep 2023

I believe there is an error in test 9. The last digit should be 3 rather than 5.

ChrisR on 3 Sep 2023

Yes, you're right. I double-counted two of the configurations. ;-)

GeeTwo on 26 Jan 2026 at 19:21

The problem statement without the images is totally inadequate without the image. I'm not going to describe the problem as I think I would write it, but just explain a bit.
All circles in this problem are the same diameter, and packed hexagonally such that every circle in the same row has the same y cartesian coordinate for its center.

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