You might be thinking of Zendo [1]. "Zendo is a game of inductive logic in which one player, the Master, creates a rule that the rest of the players, as Students, try to figure out by building and studying configurations of the game pieces. The first student to correctly guess the rule wins."
This is incredible. I copied and pasted your description into ChatGPT:
he game you're describing sounds like "Zendo," which is a game of inductive logic designed by Kory Heath. In Zendo, players use colored plastic pieces called "Icehouse pyramids" that come in different sizes and colors. The moderator, or "Master," creates a secret rule and builds two structures, one that follows the rule (marked with a white stone) and one that doesn't (marked with a black stone). The players, or "Students," then take turns building new structures and asking the Master if they follow the rule or not. The goal is for the Students to correctly guess the secret rule by observing the examples and counterexamples provided by the Master.
I live in Hungary, where I have this feeling of "fake state" getting stronger and stronger every year. I'm sure there are other similar countries.
One recent example: our education system has been neglected for long. Now, that we have an inflation of ~25% (inflation of food is around 50%), teachers literally can't make ends meet. They started to fight for themselves, and instead of taking the problem seriously, the government fights back with its power. (E.g. by firing or silencing teachers who demonstrate.) Teachers are leaving for other jobs in huge numbers. The buildings of even some of the best schools in the country are in catastrophic shape, on the brink of causing major damage to those inside. All this, because it is not a real priority to have good schools. This is only advertised, but it is a lie. The whole education system is gradually shifting into a mode of "baby sitting" kids while the parents work.
Another example is the prosecution system. Interestingly, they are very quick and effective in investigating the smallest wrongdoing if it helps those in power. If the investigation would hurt those in power, they very quickly abandon the investigation with funny and obiously fake reasons. Again: the prosecution system looks like a real one, but it's not. It has purposes different from what is officially advertised.
The closest advisor of the prime minister openly said this week, that "if you control the media, you control the thoughts of people". This, sadly, seems to be true. It really seems that the point of the government is not to run the country decently, but only to fake it. And it works.