Explaining the game "Turing Machine"

For Parts $3-5,$ you're now going to make parts of a game called "Turing Machine". Each part will be a different component of a software implementation of the game $($or a slightly trimmed down version of the game$)$ and the task descriptions will go into detail of what you have to do for each part, but it's useful to have an idea of what the physical game looks and plays like $($also$,$ it's a fun board game$).$

The Game

There is a machine which holds a secret answer $($a $3$ digit number where each digit is in the range $1-5)$ and a collection of verifiers. The goal of the player$($s$)$ is to guess the secret answer $($or better still, logically deduce the secret answer$).$

This is achieved via the verifiers. Each turn, the user guesses a $3$ digit number $($again with each digit in the range $1-5),$ and applies $3$ verifiers to that number. If the secret number shares the same property as the guessed number in relation to a verifier, the result of the verifier is "Yes" $($or True, or however you want to think about a positive response$).$ If the two numbers do not share the same property, the answer is $"$No$".$ Note that this doesn't immediately tell you what the secret number is$,$ just that it has the same "structure" as the guessed number relative to the verifier.

In the actual game, the digits of the number$($s$)$ are represented with symbols, the first digit is a blue triangle, the second digit is a yellow square and the third digit is a purple circle. For the tasks, we will replace these with x$,$ y and z respectively $($because there's no blue triangle symbol unicode$).$

A verifier is a card $($and a lookup table, but that's not on the card$)$ that describes some property that is being tested, for example:

This verifier checks if the number is even or odd

This is Verifier $5.$ It checks if the first digit is even or odd. If both the guess and answer share the same property, then the result is "Yes". So if the secret number is $123$ and the guessed number is $345,$ it will give back the answer "Yes", because both the secret number and the guess have odd first digits. If guess is instead $451,$ it will answer $"$No$",$ because the guess has an even first digit, but the secret number does not.

The results then allow logical deduction of properties of the secret number. In the example just given, both results would tell you that the first digit can only be $1,3$ or $5.$

In the board game, there are $4,5,$ or $6$ verifiers randomly chosen from a set of $48$ verifiers, and play proceeds in rounds where each player makes a guess and chooses three of the available verifiers to apply. When a player thinks they have deduced the secret number, they declare this, and look up the secret number, after which they can no longer guess. The player who correctly guesses the secret number in the fewest rounds wins.

The full rules of the board game are here. The full website will also let you play the game, though you need the verifier cards and the lookup tools $($i$.$e$.$ the actual board game$).$

The game "Turing Machine" is copyrighted by the publisher Le Scorpion Masqu$,$ and used here for educational purposes.

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