I’m going to run a round or two of the board game Turing Machine.
This game is a interesting logic puzzle. You are trying to solve a code of the form BLUE-YELLOW-PURPLE, where each color is a number between 1 to 5.
One turn of the game consists of the following steps:
You choose a 3 digit number to test, and you can choose up to 3 verifiers to test it against, and send it to me via DM.
I send you Yes or No for each of the verifiers you tested your number against.
You respond in the thread ‘Ready for Next Round’ or ‘Attempt to Solve’
If you attempt to solve and fail, then you are out of the game. If you succeed, then the game ends, and the player who solves it that round with the fewest verifier queries wins.
Some facts about the ‘verifiers’:
There will be 4 verifiers
The final code is the only possible code that will give a yes on all 4 verifiers.
You will not know to start what the verifier is testing, that information is to be deduced.
Each verifier will be testing the same question for all guesses for all players in a single game.
All games have a unique answer, if you can prove that a verifier that was testing the statement A would lead to no unique solution, then it is valid to rule out A.
How about an example:
Verifier A is “This verifier tests the parity of one of the colors.”
You submit 3-3-3 to me (remember, this is blue-yellow-purple), and ask to use verifier A.
I respond ''No".
You know the verifier is not testing ‘Blue is odd’, ‘Yellow is odd’ or ‘Purple is odd’ because if it was testing one of those statements, it would have said yes. (Note this doesn’t mean that Yellow isn’t odd in the final code, if the verifier is testing ‘Blue is even’ then it doesn’t care about your yellow number.)
Interested, sign up below by posting. I’ll start the morning after we get 5 people or on Wednesday, July 26th at the latest.
The colors are each a single digit, 1-5, so you B, C, and D ones are useless because they would give all yes, and there are no ‘all yes’ components in the box, so I’m going to go ahead and say they and statements like them do not exist as verifiers. Same with A, because verifiers aren’t that specific — they give a check to a range of answers, and it’s just the intersection of the 4 verifiers that narrows it down to one code.
The verifiers all have a theme, so you are trying to figure them out from something like 3-9 different statements.
So the parity example above has 6 statements it could be testing. (Blue is even, Yellow is even, Purple is even, Blue is odd, Yellow is odd, Purple is odd). Another verifier could be testing the relationship to one of the colors to 4, which would have 9. (B<4, B=4, B>4, and same three for Y and P).
The key thing to remember is that the verifiers DO NOT KNOW THE FINAL CODE. All they are saying is ‘Yes, your guess meets my criteria’ or ‘No, your guess does not meet my criteria’. The code is the only guess out of all 125 possibilities that gives ‘Yes’ to all 4.
Let’s go back to the parity then for one more example.
Let’s say it was testing ‘Yellow is Even’ in this game.
Any guess of the form X2X or X4X would give a check, and any guess of the form X1X, X3X, and X5X would give an X.
So I gather we would be told a class for each of verifiers, and we have to figure out what it is testing. (Well, we don’t have to, but if we don’t then we can’t be confident we have a solution.)
So suppose we started the game knowing “Verifier C tests the sum of 3 colors”. Don’t we have far more than 3 possibilities? E.g. including B+Y+P=3, =4, =5, …, =15 (or perhaps =3 and =15 are excluded as too specific), plus similar with > or <. And could it be A+B+C>=9 (though that would be equivalent to >8, and we wouldn’t care whether if was >8 or >=9)?
So we will know the class of each verifier, and a list of the possibilities we should consider for each verifier (a list that contains the actual verifier, even if other verifiers not on the list might seem to fit the class)?