Tuesday, March 27, 2018

Jigsaw Puzzles With Pre-Completed Pieces

A friend posed the following question the other day -

When you open a new jigsaw puzzle and you find a few pieces that are still connected, should you pull them apart or leave them connected and consider it a free bonus?

This was my answer:

Imagine a hypothetical example where you open the box and ALL of the pieces are connected. You could just flatten out the puzzle and it is complete. By definition, you would have to break apart the pieces in this case, because doing the puzzle requires that you visually figure out how the pieces fit together. Now imagine the same scenario, but this time only 999 of the pieces are connected. Surely any rational actor would agree that only the fool would triumphantly pop in the final piece and declare that he had done the puzzle. Continuing with this logic, you can keep reducing the size of the pre-connected clump by one. Now the question simply becomes: for what minimum value (n) would this same logic no longer apply, such that you should flip your behavior and not break up the completed pieces? I would argue that selecting any value of n greater than one would be arbitrary and capricious. Thus, you must take the pieces apart.

Sadly, my friend decided to go with the crowd consensus which was to leave the pre-connected pieces and not pull them apart. This despite nobody coming up with a counter-argument to my logic above.