The anti-intellectuals have won the war, and under the iron rule of emperor Nonotin anyone who has been deemed too smart for their own good has been brought to labour camps.
But most of the science folks turn out to have never done a fair day's work in their life, so they are worth little in the labour camps. In order to get rid of some of them, and to have a little laugh, Nonotin devises an impossible game based on an equally impossible heretic tale. Though he doesn't care much for the exact details of the tale.
He places 1 cat in each of 20 lidded boxes, and asks one of his guards to kill a random number of them. He then gathers 100 of the most useless physicists, explain this setting to them, and states the rules of the game.
The physicists will, one at a time, be taken to the room with the boxes, look into 19 of them, and then guess if the cat in the last one is living or dead. The boxes will be moved around between each visit, so the physicists will not be able to coordinate their choice of box.
If they all guess correctly they will be given their freedom, but if anyone guesses wrong they will all be executed.
The physicists only have a short while to agree on a strategy before being taken to isolation cells. They don't think it likely that they will reliably be able to hear the living cats, or otherwise identify the content of the boxes without looking.
The emperor is certain of their defeat. But is there truly nothing the physicists can do to have a fair chance of winning the game?