Turing Machine

On the Subject of Turing Machine

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

There are 4 – 6 clues labeled A – D/E/F. These clues can be displayed on the 3 vertical screens by pressing the lettered buttons below it.
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.

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.

Clue A	Clue B

Clue C	Clue D

Let’s do some testing with the clues on the previous page. First I’m going to use 121 to test with Clue A. The result of this test is an X, meaning that it did not pass the test. So that means that the 1st digit can’t be less than the 2nd digit. Then let’s try 221. This results in an X as well, which means that the 1st digit must be greater than the 2nd digit. We can deduce from this information that the 1st digit can’t be 1 and the 2nd digit can’t be 5:

1st: -2345
2nd: 1234-
3rd: 12345

Next, let’s test 112 with Clue B. This test results in an O, passing the test. That means that the sum of the 1st and 2nd digits must be less than 6. From there, we can eliminate the 5 from the 1st position and the 4 from the 2nd position:

1st: -234-
2nd: 123--
3rd: 12345

Clue C determines how many 3s are in the code. We can deduce that there can’t be 3 3s because that would make all the other clues present on this module redundant. So let’s test 222 with Clue C. This results in an X. Testing with 322 also results in an X. Which means the number of 3s in the code has to be 2. We can deduce that the 1st can’t be 4 because if it were, that would force the 2nd digit to be 3 and that would result in a sum greater than 6. We also know that the 1st can’t be 2 because that would force the 2nd digit to be 3, which makes the 1st digit less than the 2nd digit. Since the 1st digit has to be a 3, the 2nd digit can’t be a 3 because the 1st digit is greater than the 2nd. This forces the 3rd digit to be 3 since the 2nd digit can’t be a 3 and there are 2 3s in the code:

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.