“Aye aye, captain!" The perfect synchronisation of the crew rattled passing pigeons and seagulls. There's not a shadow of doubt or fear looming on anyone's face. Indeed, the voyage is only an excuse for travel - you have pinpointed the treasure island from some hidden text of antiquity. Now, it's only a matter of weeks before you reach it; and bask in its golden light!

Walking through the deck you chance across someone stealing a small nap. He has a paper chit covering his eyes - you pick it up. “Puzzle, eh?" you think, “Nothing better to spend time on."

You see that you have to write the numbers from 1 through 19 in the circles (one per circle) so that the numbers in any of the straight lines (each of these lines covers 3 circles) add up to the same number.

There are three ways of choosing the central number: consider the middle case. What is the common sum?