# 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 ≤ 5·1011
such that B(L) = 450.