This is what you imagine - competitive jigsaw puzzle solving. Individual or team. Reasonable rules against interference, assistance, cheating etc.
Assemble large groups of random volunteers. Two competitors will select people from the teams. So player A will select representatives from the random selection, as will player B. The methods of selecting people vary:
Design a school curriculum that will be put into place for a period of 50 years. At the end of the period, random (or the top) students from your school will be chosen to represent you in a puzzle solving competition. How would you design the curriculum?
A virgin planet has been discovered, with rich plant life but no animals. Design an animal weighing less than 1g; 10,000 of them will be dropped off around the planet. We will return in 1 billion years and submit jigsaw puzzles to the surviving inhabitants. Whoever's society solves them the fastest will be the winner.