# Find the correct code: Clues A .. D, 13 to open the door [closed]

This is a puzzle of a game where I know the solution, but not how it is derived. So the correct answer goes to whoever can also explain the solution.

Find the correct code:

This is written on top of a closed door:

A..D

And this is a number on the closed door: 13

On the floor the following table can be found:

A | + | 2
--+---+---
- | 3 | -
--+---+---
8 | + | D


You have to find the correct 4 digit code.

Since nobody found the solution after a week, I'm now adding a part of the correct answer as hint. If this doesn't help, I'll add the complete solution in another week.

Hint

The middle part of the code contains the 13: so A13D
A and D are replaced by single digits. But which?

• Is the door locked? If it is closed, how can we read what is written on top of it? – chasly - reinstate Monica Aug 16 '15 at 11:57
• @chaslyfromUK It's written above the door – Marwie Aug 16 '15 at 12:51
• You mean on the door-frame or on the wall above the door? Is it significant precisely where it is written? – chasly - reinstate Monica Aug 16 '15 at 12:57
• @chaslyfromUK on the wall – Marwie Aug 16 '15 at 12:59
• Is there any significance to the fact that $2^3=8$? – tfitzger Aug 17 '15 at 13:05

So my theory is it works for reading across and up and down.

So two equations with 2 unknowns:

$A+2-3-8+D=13$ and $A-8+3+2-D=13$

Simplfies to $A+D=22$ and $A-D=16$

Which rather simply goes to $A=19, D=3$

As we are looking for a 4-digit code 1903 works using 19 and 03 as the numbers. This has extra appeal as (recent) year numbers are popular 4-digit passwords.

Alternatively we are given A..D. So I propose A19D as the code as A..D has room for two more digits. I am not convinced on the code part but I think the arithmetic part is valid.

• Could it be 1903? – Gordon K Aug 16 '15 at 20:16
• Alternatively the .. Could mean that the code should be the numbers represented by B and C. However if the numbers A to D are spaced uniformly on the number line, B and C are not integers. – Gordon K Aug 16 '15 at 20:21
• @GordonK I like 1903, I was pondering it but I didn't put it into my head as 1903, I thought of it as 19 03. Years starting with 19 are rather common pin codes so that lines up nicely. I do like that better than A19D... Might put that into the answer, I just wish you didnt have to add a seemingly arbitrary number, though I suppose omitting the 3 is just as odd... As 4-digit tends to refer to numbers, I will go with 1903, but A19D is perfectly valid hex so that is somewhat interesting. – Going hamateur Aug 16 '15 at 22:33
• The code is digits only. No Hex. Unfortunately 1903 isn't the right answer. – Marwie Aug 17 '15 at 4:30
• If A..D refers to the diagonal line in the diagram running from A to D then the answer could be 19 3 3 – Gordon K Aug 17 '15 at 16:08

7133 ?

Based on the hint that:

A and D are both one digit numbers, and the code is A13D

I tried using a variation on the approach that Going Hamateur used...

I set:
A+2-3-8+D = A-8+3+2-D
A-9+D = A-3-D
D = 3
When I substituted 3 for D, I found A-6=A-6

I then applied Moonbutt74's observation that:

The Diagonal 2+3+8 = 13.I then solved A+3+D=13
D=3, so A=7

Therefore, I believe the code is:

7133

• I would be so happy just to see the correct answer because this really is making me nuts. – moonbutt74 Aug 24 '15 at 1:25
• @Marwie Is this the code? – Matthew0898 Aug 24 '15 at 19:58

A is number 11, D is number 5.

The first row A+2 = 11+2 = 13, what is written on the door.

The same is 8+D = 8+5 = 13.

For columns A-8 = 11-8 = 3, the number in the centre of table.

The same is D-2 = 5-2 =3.

So you have to type AD = 1105

• Okay upvote for the new angle, but it's the adding of the zero, that's still throwing me. – moonbutt74 Aug 20 '15 at 23:45
• @moonbutt74 I think the 0 comes because there is "A..D". Points mean that there are 4 numbers, so 05 for D – Voitcus Aug 21 '15 at 8:38