86 lines
3.4 KiB
Markdown
86 lines
3.4 KiB
Markdown
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## \-\-- Day 19: Linen Layout \-\--
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Today, The Historians take you up to the [hot springs](/2023/day/12) on
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Gear Island! Very
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[suspiciously](https://www.youtube.com/watch?v=ekL881PJMjI),
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absolutely nothing goes wrong as they begin their careful search of the
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vast field of helixes.
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Could this *finally* be your chance to visit the
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[onsen](https://en.wikipedia.org/wiki/Onsen) next door?
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Only one way to find out.
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After a brief conversation with the reception staff at the onsen front
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desk, you discover that you don\'t have the right kind of money to pay
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the admission fee. However, before you can leave, the staff get your
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attention. Apparently, they\'ve heard about how you helped at the hot
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springs, and they\'re willing to make a deal: if you can simply help
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them *arrange their towels*, they\'ll let you in for *free*!
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Every towel at this onsen is marked with a *pattern of colored stripes*.
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There are only a few patterns, but for any particular pattern, the staff
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can get you as many towels with that pattern as you need. Each
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stripe
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can be *white* (`w`), *blue* (`u`), *black* (`b`), *red* (`r`), or
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*green* (`g`). So, a towel with the pattern `ggr` would have a green
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stripe, a green stripe, and then a red stripe, in that order. (You
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can\'t reverse a pattern by flipping a towel upside-down, as that would
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cause the onsen logo to face the wrong way.)
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The Official Onsen Branding Expert has produced a list of *designs* -
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each a long sequence of stripe colors - that they would like to be able
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to display. You can use any towels you want, but all of the towels\'
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stripes must exactly match the desired design. So, to display the design
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`rgrgr`, you could use two `rg` towels and then an `r` towel, an `rgr`
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towel and then a `gr` towel, or even a single massive `rgrgr` towel
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(assuming such towel patterns were actually available).
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To start, collect together all of the available towel patterns and the
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list of desired designs (your puzzle input). For example:
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r, wr, b, g, bwu, rb, gb, br
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brwrr
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bggr
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gbbr
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rrbgbr
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ubwu
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bwurrg
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brgr
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bbrgwb
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The first line indicates the available towel patterns; in this example,
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the onsen has unlimited towels with a single red stripe (`r`), unlimited
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towels with a white stripe and then a red stripe (`wr`), and so on.
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After the blank line, the remaining lines each describe a design the
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onsen would like to be able to display. In this example, the first
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design (`brwrr`) indicates that the onsen would like to be able to
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display a black stripe, a red stripe, a white stripe, and then two red
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stripes, in that order.
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Not all designs will be possible with the available towels. In the above
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example, the designs are possible or impossible as follows:
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- `brwrr` can be made with a `br` towel, then a `wr` towel, and then
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finally an `r` towel.
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- `bggr` can be made with a `b` towel, two `g` towels, and then an `r`
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towel.
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- `gbbr` can be made with a `gb` towel and then a `br` towel.
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- `rrbgbr` can be made with `r`, `rb`, `g`, and `br`.
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- `ubwu` is *impossible*.
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- `bwurrg` can be made with `bwu`, `r`, `r`, and `g`.
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- `brgr` can be made with `br`, `g`, and `r`.
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- `bbrgwb` is *impossible*.
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In this example, `6` of the eight designs are possible with the
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available towel patterns.
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To get into the onsen as soon as possible, consult your list of towel
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patterns and desired designs carefully. *How many designs are possible?*
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To begin, [get your puzzle input](19/input).
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Answer:
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