synacor.py/notes.md

Spoilers!

Note: Codes seem to be unique for every user.

Code 1

Found in arch-spec.

== hints ==
- Here's a code for the challenge website: ............

Code 2

Obtained on initial execution of code. (Or just be lazy like me and extract it from the binary.)

Welcome to the Synacor Challenge!
Please record your progress by putting codes like
this one into the challenge website: ............

Required opcodes: nop and out

Code 3

Obtained at the completion of the self-test.

Executing self-test...

self-test complete, all tests pass
The self-test completion code is: ............

Required opcodes: All except halt and in

Code 4

At the foothills, the first area of the RPG:

== Foothills ==
Things of interest here:
- tablet

> take tablet

> use tablet
You find yourself writing "............" on the tablet.  Perhaps it's some kind of code?

Required opcodes: All except halt

Code 5 (Twisty passages)

After falling down the bridge, there is an empty lantern to the east, which should be taken. To the west, there is a passage, where one can take the ladder down or venture into the darkness. Attempting to venture into the darkness at this point will result in being eaten by Grues.

Taking the ladder down, then traversing west, south, north, a code is obtained:

Chiseled on the wall of one of the passageways, you see:

    ............

You take note of this and keep walking.

There is also a can, which can be taken and used to fill the lantern, which can then be used to become lit, and which will keep away Grues.

Code 6 (Dark passage, ruins and teleporter)

Returning to the fork at the passage and venturing to the darkness, we now continue westward to the ruins. The north door is locked, but dotted elsewhere around the ruins are a red coin (2 dots), corroded coin (triangle = 3 sides), shiny coin (pentagon = 5 sides), concave coin (7 dots) and blue coin (9 dots) which should be taken and looked at, and the equation:

_ + _ * _^2 + _^3 - _ = 399

Mathematical!

In other words, we seek a solution to the equation a + bc² + d³ - e = 399, where {a, b, c, d, e} = {2, 3, 5, 7, 9}.

Synacor being, of course, a programming-orientated exercise, the usual response to this problem is to code up a quick program to loop through all 5! = 120 permutations of the coins to find which one satisfies the equation. Being a mathematician, however – could you tell from the italics? – I will solve this the proper way: with a scientific calculator and some thinking (*insert insufferably smug expression here*).

Firstly, note that -7 ≤ a − e ≤ 7, so 392 ≤ bc² + d³ ≤ 406. Furthermore, since bc² is always positive, d³ ≤ 406. We can thus rule out d = 9, so d ≤ 7, d³ ≤ 343 and bc² ≤ 63, also ruling out c = 7 and c = 9. Furthermore, since 392 ≤ bc² + d³, d³ ≥ 329. Since we already knew d ≤ 7, d = 7.

Consequently, 49 ≤ bc² ≤ 63. It is trivial to check that no solutions satisfy this for c = 2 and c = 3, so c = 5 and b = 2. The values of a and e are now easily found.

The solution is:

9 + 2 * 5^2 + 7^3 - 3 = 399

BOOM!

(Well, actually all I did the first time was get up to d ≤ 7, then use guess and check.)

The coins should therefore be used in the order: blue, red, shiny, concave, corroded.

Proceed to the north door and use the teleporter to obtain the code:

== Ruins ==
Things of interest here:
- teleporter

> use teleporter
You activate the teleporter!  As you spiral through time and space, you think you see a pattern in the stars...

    ............

After a few moments, you find yourself back on solid ground and a little disoriented.