Turing Machine

The Sandbox Games
1

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:

  1. 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.
  2. I send you Yes or No for each of the verifiers you tested your number against.
  3. 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’:

  1. There will be 4 verifiers
  2. The final code is the only possible code that will give a yes on all 4 verifiers.
  3. You will not know to start what the verifier is testing, that information is to be deduced.
  4. Each verifier will be testing the same question for all guesses for all players in a single game.
  5. 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.

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2

I’m totally lost. Are there any constraints on verifiers? As an extreme, would these be ok

A: The code is 135.
B: Blue < 10
C. Blue < 20
D. Blue < 50

There is only one code that would get a yes to all three, but chances we would get it before losing interest is tiny.

And in your example, what guesses would be a yes if Verifier A were testing the parity of one of the colors?

3

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.

4

Also, once people are used to it, the game seems to end after 3 rounds most of the time, with the winner being the once that only needs 1 or 2 verifiers to figure it out.

Starting with round 3, I’ll let people request 1 verifier result at a time in case they want to see the answer before deciding if they need more info.

5

I love that game, definitely in. I’ve found some of the harder puzzles make it to round 4

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6

I’d be interested, but I’m on vacation until 8/1 and I may not be able to check the thread that often from 7/26 through 7/31.

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7

How much time commitment would this be? I could probably only commit to 2, maybe 3 turns per day.

8

Love this game.
Just played our copy this past weeken with a few old AOers.

Sadly i do not think i have time to play along online, but i hope you get some good participation.

9

I was thinking only 1 round a day max unless the players moved it along faster.

10

I’ll give it a try, though I’m not great at these types of puzzles. At a minimum, I will give everyone else someone to beat :slight_smile:

11

Talk about setting a pretty low bar . . .

:stuck_out_tongue:

12

I’m going to sit out and watch this round. School starts next week.

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13

I remain confused. Is “This verifier tests the parity of one of the colors.” literally what verifier A is,

Or is Verifier A one and only one of those 6 statements?

And if Verifier A is one and only one of those 6 statements, is it true that every Verifier tests a single color? (E.g. could a Verifier be “Blue > Yellow”? Not valid if they can test a single color).

14

At the start of the game, all you know is that the verifier is testing the parity of one of the colors.

During the game, you should be able to deduce that in this particular game it is testing ‘Yellow is even’ (or ‘Blue is odd’ ,or whichever it actually is for the game).

Some verifiers that I’ve seen could be testing the relationship between 2 of the colors (B below), or the sum of 3 colors (C below)or something like that.

There are 48 in the game box, so I haven’t gone through all of them, but some other examples above.

B could be one of nine statements in any particular game B>Y, B=Y, B<Y, B>P, B=P, B<P, Y>P, Y=P,Y<P — again it’s on the player to eliminate what it could be testing.

C would only have 3 options … maybe B+Y+P < 6, B+Y+P = 6, or B+Y+P >6.

15

It’s getting clearer, but haze remains.

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)?

16

The wording on those seem to always be 'the sum of 3 colors in comparison to a given number. I don’t think any of the verifiers have more than 9 options from what I’ve seen.

17

And when I realize the actual game verifiers, I’ll give both the theme and the actual options.

18

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)?

That’s much clearer. I’ll give it a shot.

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19

Yeah, the game is more figure out what statement each verifier is testing from all of its’ class, AND then figuring out what is the only code that gives a yes to each of the actual statements.

20

So, at the start of the game, players will be told something like the following?

Verifier 1 tests the parity of one of the colors.

Verifier 2 tests the relationship between two of the colors.

Verifier 3 tests the sum of the three colors relative to 9.

And it’s on the players to know what the possible tests could be.