A third class plays using a consensus model based on explicit relationships of trust.
Each student keeps track of which of the others they consider trustworthy. Since they all play together everyday, they know who is nice, and who is naughty.
When a supermajority trusts the student placing a new block, that student is allowed to place it anywhere.
When not enough people trust the student placing the block, they prevent that person from doing so. That person may try again, but until they're willing to play nice and act trustworthy, they cannot place any blocks. They sit in the corner and pout until they come to their senses.
No one has to solve any puzzles, or roll any dice.
The tower is built efficiently, and all sorts of interesting designs are made by the creative energy that would have otherwise been wasted on busywork.