The game show The Price is Right has a game called The Race Game . You’re shown four prizes and four prices and you need to match the prices to the correct prizes. After you place each price tag next to a prize, you run back and pull a lever on this machine that shows you how many prices you have correct (0,1,2, or 4). You continue switching prices until you get all four correct or the 45 second clock expires.
You can set/change the price tags and pull the lever in about an 8 second round-trip, so you have a maximum of about 5 tries, maybe 6 if you’re fast. The question I have is: Assuming you have no idea about the prices of the prizes, and given that you have at most 6 guesses, is is possible to guarantee a win?
In more technical terms, if you graph the complete set of possible guesses and possible solutions, is the maximum height of the tree more than six?
To find this, I’d like to write a program to show me the best solution to minimize guesses.