Pagoda

From BoardGameGeek:

From the box: The classic Chinese game of tower building On each turn try to complete the tower on the purple base. One move allows you to break a stack at any point and place it on another... ... but you must have your three sections one on top of the other to win! Components: 12 tower sections, 3 each in 4 colours 1 roof 1 purple base 1 game board 1 die Based tenuously on the tower of Hanoi, each player has 3 tiers in their colour, and attempts to assemble the complete tower. They get a number of actions determined by the die, and only win if they can (a) assemble the complete stack, and (b) have all their pieces together.