In general you have a number of inputs, a,b,c,d etc, and a number of outputs A, B, C, D etc. The outputs can exist in a number of different states, A0, A1, A2 etc. The 'rules' of the game determine which outputs have their state changed by each input. eg a raises A, B and C. b raises B and C. c raises C. The object of the game is then to apply each input once in the right order, so as to maximise the state of each output. In this simple case it would be c,b,a. Outputs can have different maximum states. To allow for greater variation, more complex rules can also be used, in which the state of one of the outputs is a factor. eg a raises B if A>2. Branching paths can also be introduced by allowing more outputs than inputs, and allowing 'horizontal' transitions such as "b changes A to E if A<3". You could generalise further to allow inputs to lower the state of outputs too, and also set specific completion requirements, eg Maximise A and B, while Minimise C.
There are lots of ways this mechanism could be used in a thought test. Here are 2, just to illustrate the pros and cos of different impementations.
As a nice variation to the pet idea, rather than have everything take place at a building built by the designer, allow the pets to be transportable. Each designer creates 7 identical pets, which are then passed from person to person. Support?