data/problems/354.yml
---
:id: 354
:name: Distances in a bee's honeycomb
:url: https://projecteuler.net/problem=354
:content: "Consider a honey bee's honeycomb where each cell is a perfect regular hexagon
with side length 1.\n\n ![p354_bee_honeycomb.png]({{ images_dir }}/p354_bee_honeycomb.png)\n\nOne
particular cell is occupied by the queen bee. \nFor a positive real number <var>L</var>,
let B(<var>L</var>) count the cells with distance <var>L</var> 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. \nFor
example, B(√3) = 6, B(√21) = 12 and B(111 111 111) = 54.\n\nFind the number of <var>L</var>
≤ 5·10<sup>11</sup> such that B(<var>L</var>) = 450.\n\n"