Gate To Enlightenment

Here we are. The hidden entrance to the headquarters of the forgotten Brotherhood of Maat.

Won't budge.

At least the door matches the old sketch from the manuscript.

I'll bet these two seals I found nearby can shed some light on the matter.

• Yes, the blocks need to be inserted into the door in the correct order, in order to open it;

• No, I can't just try all the combinations, since the door might be booby-trapped;

• All clues and blocks are right-side-up. There's no need to turn anything around.

• I love this but what exactly are we supposed to do? Apr 7, 2016 at 17:19
• @BeastlyGerbil find out how to get the door open. Apr 7, 2016 at 17:20
• I cast Summon Troll and have him bash the door in. Apr 7, 2016 at 18:33
• @ChrisCudmore the trolls are all busy commenting on YouTube Apr 7, 2016 at 18:35
• @Yehuda: I'm loving your puzzles so far, especially this one and "The Markings of Mictal"! Wish there was some way to give you a bounty for a question :/
– Deusovi
Apr 9, 2016 at 6:15

After careful examination of the seals, the sketch, and the inscription on the door, you try:

the combination | |||| ||| ||||| || (1 4 3 5 2)...!

Looking at the seals,

you notice that on each row, the first three symbols and the last three appear oddly similar, save for some specific difference. You suspect that the center symbols might indicate some kind of operation performed on the first three symbols that results in the last three.

Examination of the sketch confirms your suspicions. The symbols above the door are a list of operations that will reveal the key!

Returning to the seals, you determine the following:
The line and the dot appended to some symbols are cursors, indicating where and how certain operations are meant to be performed.

You interpret the operators as follows:
1. = : Adds two lines to the number above the dot. (Noting that the final code requires two of these operations and that the sketch shows three of these operations, you suspect that this operation fails at some point. Perhaps if the number is already too large?)
2. < and > : Rotates the entire sequence in the given direction, moving the cursor, by the number of positions indicated by the following symbol (either a set of lines or a ^).
3. v : Places/moves a cursor to the position indicated by the following symbol (either a set of lines or ^).
4. ^ : Reads the number above the cursor. This is used to the right of one of the previous operators.

You also note that all operators (except =) default to using the line cursor but will use the dot cursor if a dot is added to the operator.

Therefore the seals list the following operations (using [] to indicate the line cursor and () to indicate the dot cursor):

First seal:
Add two lines to # at dot; [2] (1) 0 => [2] (3) 0
Place dot cursor at position 2; [0] 0 0 => [0] (0) 0

Second seal:
Rotate line cursor right by 2 positions; [a] 0 0 => 0 0 [a]
Rotate line cursor left by 1 position; 0 0 [a] => 0 [a] 0
Place line cursor at position 1; 0 0 0 => [0] 0 0
Rotate line cursor right by [line = 1] positions; [1] 0 0 => 0 [1] 0
Place line cursor at position [line = 2]; [2] 0 0 => 2 [0] 0

Therefore, you determine the combination as follows:

Starting with the symbols on the door:
3 2 1 2 3

1. Place line cursor at position 1.
[3] 2 1 2 3

2. Place dot cursor at position [line = 3].
[3] 2 (1) 2 3

3. Rotate line cursor right by (dot = 1) positions. (Note: dot cursor remains at the same position)
3 [3] (2) 1 2

4. Place line cursor at position [line = 3].
3 3 [(2)] 1 2

5. Place dot cursor at position [line = 2].
3 (3) [2] 1 2

6. Add 2 to the number at the dot cursor.
3 (5) [2] 1 2

7. Rotate dot cursor right by (dot = 5) positions. (Does nothing)
3 (5) [2] 1 2

8. Place line cursor at position (dot = 5).
3 (5) 2 1 [2]

9. Add 2 to the number at the dot cursor. (Fails because it would exceed 5)
3 (5) 2 1 [2]

10. Place line cursor at position [line = 2].
3 [(5)] 2 1 2

11. Place dot cursor at position (dot = 5).
3 [5] 2 1 (2)

12. Add 2 to number at dot cursor.
3 [5] 2 1 (4)

13. Rotate dot cursor left by [line = 5] positions. (Again, does nothing)
3 [5] 2 1 (4)

14. Place line cursor at position [line = 5].
3 5 2 1 [(4)]

15. Rotate line cursor right by 2 positions.
1 [4] 3 5 (2)

Therefore the combination must be 1 4 3 5 2!

• Seal 1, line 2: the operator v that you claim always come with another is alone. How you you explain it? Apr 9, 2016 at 8:45
• I'm not sure I understand? In seal 1, line 2, the operator I refer to is the dotted v followed by two lines (meaning 2). Apr 9, 2016 at 9:09
• Well done! Single correction: the "=" means adding the value of the _ cursor (although that wasn't clear from the seals. I guess I should have added another line to clarify that one). Apr 9, 2016 at 19:03