93 lines
4.0 KiB
Markdown
93 lines
4.0 KiB
Markdown
# Spoilers!
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Note: Codes seem to be unique for every user.
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## Code 1
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Found in `arch-spec`.
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== hints ==
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- Here's a code for the challenge website: ............
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## Code 2
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Obtained on initial execution of code. (Or just be lazy like me and extract it from the binary.)
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Welcome to the Synacor Challenge!
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Please record your progress by putting codes like
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this one into the challenge website: ............
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Required opcodes: `nop` and `out`
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## Code 3
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Obtained at the completion of the self-test.
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Executing self-test...
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self-test complete, all tests pass
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The self-test completion code is: ............
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Required opcodes: All except `halt` and `in`
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## Code 4
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At the foothills, the first area of the RPG:
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== Foothills ==
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Things of interest here:
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- tablet
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> take tablet
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> use tablet
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You find yourself writing "............" on the tablet. Perhaps it's some kind of code?
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Required opcodes: All except `halt`
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## Code 5 (Twisty passages)
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After falling down the bridge, there is an `empty lantern` to the `east`, which should be `take`n. 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.
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Taking the `ladder` down, then traversing `west`, `south`, `north`, a code is obtained:
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Chiseled on the wall of one of the passageways, you see:
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............
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You take note of this and keep walking.
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There is also a can, which can be `take`n and `use`d to fill the lantern, which can then be `use`d to become lit, and which will keep away Grues.
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## Code 6 (Dark passage, ruins and teleporter)
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Returning to the fork at the passage and venturing to the `darkness`, we now `continue` `west`ward 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 `take`n and `look`ed at, and the equation:
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_ + _ * _^2 + _^3 - _ = 399
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### Mathematical!
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In other words, we seek a solution to the equation *a* + *bc*<sup>2</sup> + *d*<sup>3</sup> - e = 399, where {*a*, *b*, *c*, *d*, *e*} = {2, 3, 5, 7, 9}.
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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](https://xkcd.com/435/): with a scientific calculator and some thinking (\*insert insufferably smug expression here\*).
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Firstly, note that -7 ≤ *a* − *e* ≤ 7, so 392 ≤ *bc*<sup>2</sup> + *d*<sup>3</sup> ≤ 406. Furthermore, since *bc*<sup>2</sup> is always positive, *d*<sup>3</sup> ≤ 406. We can thus rule out *d* = 9, so *d* ≤ 7, *d*<sup>3</sup> ≤ 343 and *bc*<sup>2</sup> ≤ 63, also ruling out *c* = 7 and *c* = 9. Furthermore, since 392 ≤ *bc*<sup>2</sup> + *d*<sup>3</sup>, *d*<sup>3</sup> ≥ 329. Since we already knew *d* ≤ 7, *d* = 7.
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Consequently, 49 ≤ *bc*<sup>2</sup> ≤ 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.
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The solution is:
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9 + 2 * 5^2 + 7^3 - 3 = 399
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**BOOM!**
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(Well, actually all I did the first time was get up to *d* ≤ 7, then use guess and check.)
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The coins should therefore be `use`d in the order: `blue`, `red`, `shiny`, `concave`, `corroded`.
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Proceed to the `north` door and `use` the `teleporter` to obtain the code:
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== Ruins ==
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Things of interest here:
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- teleporter
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> use teleporter
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You activate the teleporter! As you spiral through time and space, you think you see a pattern in the stars...
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............
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After a few moments, you find yourself back on solid ground and a little disoriented.
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