Diadem

Note that this is a different game than the galactic empire game of the same name by Fantasy Games Unlimited. Diadem is a multi-player puzzle game by Reinhold Wittig. The is made up of six plastic pieces, each with three hexes and each of these has two holes. The pieces are placed together to form a ring, and players place colored pegs in the holes in a way such that no same-color pegs can be next to each other. After the board is filled, the three pieces are separated and spun, and the players try to put them back together meeting the same condition.