Draw one of the two possible diagonals in every cell. All internal corners (where four cells meet) are connected to the outer edge of the grid through some drawn diagonals (in other words, do not draw any closed loop of diagonals). A number on a cell corner indicates how many drawn diagonals should directly touch that corner.
(Rules and example from PGP IB)
History of the puzzle
First appeared in Nikoli volume 103 (2003). Invented by チェバの定理 ("Ceva's Theorem"). Original title ごきげんななめ means "in a bad temper" and is a composite word made from ごきげん ("mood") and ななめ ("tilted").