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How do you solve it in just six questions?

Posted: 17 February 2024, 12:43
by Rothion
Hello, everyone...
Since I am a non-English speaking person, I got help from Google to write in English.
I hope you will be lenient if there are any problems with grammar.

I play Turing Machine by solo game.
https://boardgamearena.com/5/turingmach ... =476259555

I find answer in 9 questions.
but, Machine find in 6 questions.

I don't understand to Machine's solve.
I feel like there's something missing in solving this game.
Please tell me, what I'm "missing" to beat the Machine.

I proceeded with the solution as follows.

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First of all, "C2" and "F2" verifiers are incompatible.
(The upper card of each verifier will be referred to as number 1, and the lower card as number 2.)
This is because both verifiers show a correlation between a square and a certain number.
Once one verifier is decided, the verifier on the other side will be useless.
And, “F1” verifier and “D2” verifier are also the same.

So, I decided to focus on the "F" verifier.
It is not "F11" here.
Because the number of cases is too small.

124 > [ A B F ] > [ ✔️ ✔️ ✖️ ]
>> A is "A11" or "A21"
>> B is "B13" or "B21"
>> F is "F13" or "F22" or "F23"

132 > [ C E F ] > [ ✖️ ✔️ ✖️ ]
>> F is "F23" (Square is greater than 3.)
>> E is "E13" or "E21"
>> C is "C11" (There are more even numbers than odd numbers.)

I knew a lot, but there didn't seem to be much I could deduct to find the answer.

512 > [ D E ] > [ ✖️ ✔️]
>> E is "E13" (It is not in ascending or descending order.)
>> D is "D12" or "D21" // “D23” was deducted due to insufficient number of cases.

Now, I focus on the "D" verifier.
"There are no consecutive numbers arranged in ascending or descending order." is too many cases.
The square was still either 4 or 5, and this proposition did not sufficiently reduce the number of cases.
Since there must be only one correct answer, "the circle is an odd number."

Now, I focus on the "B" verifier.
I found that this verifier always makes a triangle into 2 and a square into 4 even if it is not determined.
Because the circles are odd, the remainder is even. (C11)
"B13" and "B21" have something in common in that the triangles and squares refer to different numbers.
So I decided that the "A" verifier could solve everything.

If "A11" then, 243.
if "A21" then, 241.
245 cannot be the answer because it is in ascending order. (E13)

512 > [ A ] > [ ✖️ ]
>> A is "A11" (A triangle is smaller than a circle.)

I find answer 243.
but, Machine is find in 6 questions.
I lost to the Machine.

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 14:50
by Romain672
Since you shared on the forum, I took some time on my solver, I hope I didn't made a mistake. Here is all the solutions:
abc def: solution(s)
111 111: 142/425
111 112: 243/423
111 121: 234/314
111 122: 254
111 221: 235/245
111 222: 353/354
112 111: 314
112 221: 235/245

121 111: 152
122 111: 322
122 211: 344

211 111: 342
211 112: 241/425
211 121: 152/552
211 221: 445/455
211 222: 221/251
212 121: 115/452
212 221: 245

221 111: 352
221 121: 552
222 121: 225
222 211: 231

Solutions in order:
- 115/142/152/152
- 221/225/231/234/235/235/241/243/245/245/245/251/254
- 314/314/322/342/344/352/353/354
- 423/425/425/445/452/455
- 552/552

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 15:18
by Rothion
Romain672 wrote: 17 February 2024, 14:50
abc def: solution(s)
111 111: 142/425
Can I think of these as the only results that can come out of a bundle of verifiers?

For example,
"111 111: 142/425" is....
A : Compare blue and purple.
B : Verifies whether there are repeating numbers.
C : Compare the number of times an even number appears with the number of times an odd number appears.
D : Verifies whether purple is even or odd.
E : Verifies whether the three numbers in the code are in ascending, descending, or neither order.
F : Verifies that there are consecutive numbers arranged in ascending order.
....then, answer must be 142 or 425.

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 15:36
by Romain672
Exactly yes. Number of solutions without asking any questions.

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 16:07
by Rothion
Interesting.....
Very very interesting......
great job.
I think I need to think a little more about how to use this.

I doubt it's possible for humans in practice, but I think..... might be able to get something general.

It's midnight where I live.
I have to sleep.
I'll think about it tomorrow.

thank you.

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 17:00
by Jellby
I got a total of 30 possible solutions (some solutions are the same code, but still more than 16 possible codes), which would need at least 5 questions (2^4 < 30 < 2^5) to solve any possible case. Probably more if not every card can be disambiguated with one question.

I have the feeling the "machine" solution is just a semi-arbitrary number based on the number of cards.

Re: How do you solve it in just six questions?

Posted: 17 February 2024, 18:49
by Flibberdyjib
Hi, there is actually a bug on BGA that sometimes it does not report the correct number of questions for the machine.

If you search the game # E64 CAD 3 on the official website https://turingmachine.info/, then it actually took the machine 3 rounds and 9 questions.

Re: How do you solve it in just six questions?

Posted: 18 February 2024, 01:00
by Rothion
Flibberdyjib wrote: 17 February 2024, 18:49 Hi, there is actually a bug on BGA that sometimes it does not report the correct number of questions for the machine.

If you search the game # E64 CAD 3 on the official website https://turingmachine.info/, then it actually took the machine 3 rounds and 9 questions.
Oh..........
Uh..........
Hmm.......
Oh God....

thank you.