I must issue a word of caution dear traveler. As your journey nears its end, you have one final obstacle to overcome. Ahead lies the gate of the guardians. As you might suspect, the gate is protected by two guardians. One always lies and one always tells the truth. In order to ensure your safe passage across the threshold of the gate, you must determine their password.

Each guardian only knows the other's half of the password along with how to determine their own. They will supply this information to you upon request.

However, there is one very important rule: you may only speak to one of the guardians. Choose wisely dear traveler, for this decision, could very well be your last.

As you approach the gate you notice an inscription:

This gate is equidistant from the farthest edges of the world.

Note: Please follow the rules and only read the section for one of the guardians. While there's no shame in looking at both, the puzzle is more fun to solve by the rules. If you do look, let us know when you chose to do so in your answer, you won't be disqualified.

##### Left Guardian

You approach the guardian on the left:

Ahhh, wise choice dear traveler.

I always tell the truth.
Nineteen, five, twenty. Start in the middle of a icosikaihexagon; two, seven, seven.

##### Right Guardian

You approach the guardian on the right:

Ahhh, wise choice dear traveler.

I always tell the truth.
Six, fifteen, six. Navigate between the edges of two dodecagons; six, seven, eight.

After approaching the guardian of your choosing and hearing what they have to say, both guardians sternly demand; what's the password?!

Note: Your answer must include which guard you spoke with, and your determination on whether or not they were the liar, along with what the password is, in order to get the checkmark.

• Is the geometry tag also needed? Commented Oct 9, 2021 at 10:06
• Also, are the units of the passwords that determine their length only digits, with the numbers they're telling being different segments, or are their numbers the units whether they're single digits or not? Commented Oct 9, 2021 at 10:16
• I think, Puzzle has confusing and requires some clarity: (A) Is there 1 Password or 2 ? (B) Assuming 1 Password, which half goes with which Guardian ? If we have to figure that out, better to mention explicitly. (C) It says to "choose the Guardian wisely", but what criterion is available to the traveler to make a wise choice rather than random choice ? (D) Is either one Guardian enough to figure out the unique Password ? (E) Unlike stating "1+2=3" or "I am not a Guardian", the Guardians just give 3 numbers and then give Instructions which can be called neither truth nor lies ....
– Prem
Commented Oct 10, 2021 at 8:24
• A: 1; B: that’s part of the puzzle, they know the other guardian’s half, and how to solve their own half; C: that’s just part of the story, there is no wise choice; D: yes, either guardian allows you to find the password, however 1 is lying (e.g only giving semi accurate information); E: when the method of solving is determined, you will know your whether or not your guardian was lying. Commented Oct 10, 2021 at 12:12
• @Prem see the above since I forgot to mention you. Commented Oct 10, 2021 at 12:46

Left Guardian is ...

... telling the truth.
We have 26 sides on the icosikaihexagon and we have the 26 English letters.
19 5 20 == SET
2 7 7 ROT13 == 15 20 20 == OTT

Right Guardian is ...

... lying, because we know one of them lies.
More-over, we have 24 sides on the 2 dodecagons but we have the 26 English letters.
Hence, it will not work.
UNRESOLVED PROBLEM : But, if this was the choice, the traveler seems doomed !

• You're very close. Caesar isn't involved here, think about the clue equidistant and how it relates to the left guardian's message. Commented Oct 10, 2021 at 14:40
• Still thinking .... Maybe, X Y Z means start ( where ?? ) and go X sides ahead, then Y sides ahead and then Z sides ahead .... Maybe, start between M & N , hmmm ....
– Prem
Commented Oct 10, 2021 at 15:44
• Try starting with M. Commented Oct 10, 2021 at 16:29