Problem 354

Distances in a bee's honeycomb

Consider a honey bee's honeycomb where each cell is a perfect regular hexagon with side length 1.

One particular cell is occupied by the queen bee.

For a positive real number `L`, let B(`L`) count the cells with distance `L`
from the queen bee cell (all distances are measured from centre to
centre); you may assume that the honeycomb is large enough to
accommodate for any distance we wish to consider.

For example, B(3) = 6, B(21) = 12 and B(111 111 111) = 54.

Find the number of `L` 5·10^{11} such that B(`L`) = 450.

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These problems are part of
Project Euler
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CC BY-NC-SA 2.0 UK
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