Many thanks to Jens Voss for suggesting this problem. 

Label the hexagonal entries of the honeycomb on the left with the integers from 1 to 19, each integer used only once, in such a way that the sum of the entries in each diagonal is constant throughout.  The diagonals run in three directions; note that some diagonals have three, some four, and some five hexagons.

(Click here if you want to know what that magic sum should be.) 

For the more adventurous: This problem asks about a honeycomb having three concentric rings of hexagons. You can ask the same question about an n-ringed honeycomb. What would be the constant sum for an n-ringed honeycomb? For which values of n does an n-ringed honeycomb exist?