Pagoda (1996)

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.