-- Nancy will say that she saw a picture like this in the lighthouse. (If you don't remember it, face the hatch and look to your left.) After you deal with your surprise guest --
-- come back to the lighthouse and click on the flower picture to see what's what.
There's a reference to this new puzzle in "Magnus's note," though it's not much help. Read to the end of this hint for the solution.
This puzzle is sort of like a triangular sudoku, only some of the horizontal or diagonal rows have only 8 or 9 spaces instead of 10. In those rows, you can't use all the digits, and you can't have any repeats in the digits you do use.
Still, the same basic strategies apply. Look first for a triangle or row that's only missing one digit and add it in. If there aren't any like that, look for a triangle with two missing digits and check the intersecting rows to see which one goes where.
And so on in that fashion. The main difficulty of this array is remembering all the possible directions you have to look. You might find it easier to keep track by using a piece of paper against the screen to follow the lines.
When you have a triangle completely filled up, its border lights up. The lights around the outside come on when those rows are correctly filled.