Turing Machine Nightmare

On the Subject of Turing Machine Nightmare

British mathematician and cryptanalyst Alan Turing made a significant contribution to the advent of computers.

If the module background is white, then you’re looking at Turing Machine.

There are 4 – 6 clues labeled A – D/E/F. These clues can be displayed on the 3 vertical screens by pressing the vertical screens.
The numbered buttons allows you to input a 3 digit code onto the smaller screen in the top right corner.
Pressing a lettered button while a 3 digit code is displayed will test that code with the clue you pressed and print the results on the screen in the bottom right corner.
Pressing the smaller screen will submit the displayed 3 digit code, checking if the code passes every clue.
Determine the 3 digit code using the clues and submit it to disarm the module.
Submitting an incorrect code will result in a strike and the module will generate a new puzzle.

Code

The code is made up of 3 digits between 1 and 5.
You can’t test the same code twice until you tested all 125 possible combinations.
After testing 125 codes, the module will reset its internal counter and allow you to test previous codes.

Clues

Each clue is made up of 3 screens.
The left and right screens will be a value, whether its a number or referring to the 3 digit code.
The middle screen is a comparator which compares the value(s) on the left to the value(s) on the right.
Each clue will have exactly 1 screen (mostly) that will contain more than 1 clue element.
A screen containing multiple clue elements will be separated in to 2 – 3 rows.
The clue will be using one of these clue elements to determine what the 3 digit code is.
Each clue is labeled with a letter but you don’t know which clue is tied to which letter.

NOTE: All the clues are needed to determine the code. No clue will repeat itself.

Clue Elements

Number (0 – 15)	1st digit	2nd digit	3rd digit
Number of occurrences of that number	1st and 2nd digits	1st and 3rd digits	2nd and 3rd digits
Sum of the 1st and 2nd digits	Sum of the 1st and 3rd digits	Sum of the 2nd and 3rd digits	Sum of all 3 digits
Absolute difference of the 1st and 2nd digits	Absolute difference of the 1st and 3rd digits	Absolute difference of the 2nd and 3rd digits	Number of distinct numbers.
Number of consecutive pairs	Code is in ascending order	Code is in descending order	Code is in chaotic order
Number of even numbers	Number of odd numbers	Less than	Equal to
Greater than	Divisible by	Not divisible by

When a screen is displaying multiple clue elements for a symbol, it will look like the picture on the left. When a clue is displaying multiple clue elements for a number, it will look like the picture on the right. The list of clue elements for a number is all the numbers between those 2 numbers, including the ones on the screen.

Since we don’t know which clue is labeled with what letter, we have to change our testing strategy. While I was playing with the puzzle, I find it best to do 2 tests that would result in a 50/50 split where half of the clues could be that letter and the other half couldn’t possibly be that letter. The 2 codes I will test is 222 and 414, this should be enough to cause a 50/50 split between the TL and BR clues:

222: A O
414: A O

From this, we can deduce that the clues in the TL and BR are not labeled A. Now we just need to do 1 more test that would show a difference between the TR and BL clues:

213: A O

Now that we add a 3 to the code and it still passes, we can deduce that it can’t be the BL clue. The TR clue is the clue we’ve been testing all along and now we know that the 1st + 2nd digits must be less than 6.

1st: 1234-
2nd: 1234-
3rd: 12345

Now I’m going to test the numbers 125 and 225 with B:

125: B X
225: B X

We can deduce that the BR clue is not labeled B and so far we tested 0 threes and 1st digit is less than or equal to the 2nd digit:

425: B X

This means that the BL clue is labeled B. I’ll do one more test to see how many threes are in the code:

523: B X

Now we know that there has to be 2 threes in the code since the tests came out negative for a number of threes below 2. It can’t be 3 threes otherwise it would make the rest of the clues superfluous. If the 1st or 2nd digit is a number higher than 3, the other digit has to be a three according to the 2 threes rule, violating the 1st + 2nd digit is less than 6 rule.

1st: 123--
2nd: 123--
3rd: 12345

Next, let’s figure out what clue C is:

344: C X

Just by doing this 1 test, we can deduce that this clue refers the the TL clue. If the 1st digit is equal to the 2nd digit, that would mean that both of them have to be threes, violating the 1st + 2nd is less than 6 rule. That means that the 1st digit must be greater than the 2nd digit.

1st: --3--
2nd: 12---
3rd: --3--

Finally, let’s determine Clue D. We know that the clue can’t reference the 1st + 3rd clue element since we know both the 1st and 3rd digit has to be 3. So either this clue refers to 1st + 2nd or 2nd + 3rd. It doesn’t matter which one it is because all we need to determine is if the 2nd digit is 1 or 2. Considering the clue is about being greater than 4 and both the 1st and 3rd digits are 3, that forces the 2nd digit to be 2. The solution to this puzzle should be 323.

Clarifications

When the keyword AND is being used in the example on the left, it means that BOTH of those positions must fulfill the given clue. In this case, the number 4 has to be greater than both positions, which can also translate to both positions must be less than 4.

The clue on the right is the exception to when a clue has exactly 1 screen that shows multiple clue elements. Treat each row as 1 criteria like so: 1st is less than 2nd and 3rd | 2nd is less than 1st and 3rd | 3rd is less than 1st and 2nd.

The number of distinct numbers is equal to number of different values. A code of 111 would have 1 distinct number, 112 would have 2 distinct numbers, and 123 would have 3 distinct numbers.

A consecutive pair is a pair of numbers that are adjacent and have a absolute difference of 1. A code of 114 has 0 consecutive pairs, 132 has 1 consecutive pair, and 545 has 2 consecutive pairs.

When a clue refers to order, it will compare it to a value of 0 or 1. What the clue is checking is the absence(0)/presence(1) of that order in the code.

A code is in ascending order when the Nth digit is less than the (N + 1)th digit: 135, 245, 123, etc.

A code is in descending order when the Nth digit is greater than the (N + 1)th digit: 431, 521, 321, etc.

A code is in chaotic order when its neither in ascending or descending order: 154, 312, 224, etc.

A number is considered divisible by another number if the result doesn’t contain any decimal places. 12 is divisible by 1, 2, 3, 4, 6, and 12. 12 is not divisible by 5, 7, 8, 9, 10, and 11.