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Advent of Code
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--- Day 19: Linen Layout ---
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Today, The Historians take you up to the [16]hot springs on Gear Island!
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Very [17]suspiciously, absolutely nothing goes wrong as they begin their
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careful search of the vast field of helixes.
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Could this finally be your chance to visit the [18]onsen next door? Only
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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 the
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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 them
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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 stripe can
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be white (w), blue (u), black (b), red (r), or green (g). So, a towel with
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the pattern ggr would have a green stripe, a green stripe, and then a red
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stripe, in that order. (You can't reverse a pattern by flipping a towel
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upside-down, as that would cause the onsen logo to face the wrong way.)
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The Official Onsen Branding Expert has produced a list of designs - each a
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long sequence of stripe colors - that they would like to be able to
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display. You can use any towels you want, but all of the towels' stripes
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must exactly match the desired design. So, to display the design rgrgr,
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you could use two rg towels and then an r towel, an rgr towel and then a
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gr towel, or even a single massive rgrgr towel (assuming such towel
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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 onsen
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would like to be able to display. In this example, the first design
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(brwrr) indicates that the onsen would like to be able to display a black
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stripe, a red stripe, a white stripe, and then two red stripes, in that
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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 finally
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an r towel.
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• bggr can be made with a b towel, two g towels, and then an r 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 available
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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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Your puzzle answer was 311.
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--- Part Two ---
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The staff don't really like some of the towel arrangements you came up
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with. To avoid an endless cycle of towel rearrangement, maybe you should
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just give them every possible option.
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Here are all of the different ways the above example's designs can be
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made:
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brwrr can be made in two different ways: b, r, wr, r or br, wr, r.
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bggr can only be made with b, g, g, and r.
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gbbr can be made 4 different ways:
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• g, b, b, r
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• g, b, br
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• gb, b, r
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• gb, br
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rrbgbr can be made 6 different ways:
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• r, r, b, g, b, r
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• r, r, b, g, br
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• r, r, b, gb, r
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• r, rb, g, b, r
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• r, rb, g, br
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• r, rb, gb, r
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bwurrg can only be made with bwu, r, r, and g.
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brgr can be made in two different ways: b, r, g, r or br, g, r.
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ubwu and bbrgwb are still impossible.
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Adding up all of the ways the towels in this example could be arranged
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into the desired designs yields 16 (2 + 1 + 4 + 6 + 1 + 2).
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They'll let you into the onsen as soon as you have the list. What do you
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get if you add up the number of different ways you could make each design?
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Your puzzle answer was 616234236468263.
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Both parts of this puzzle are complete! They provide two gold stars: **
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At this point, you should [19]return to your Advent calendar and try
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another puzzle.
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If you still want to see it, you can [20]get your puzzle input.
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References
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Visible links
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1. https://adventofcode.com/
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2. https://adventofcode.com/2024/about
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3. https://adventofcode.com/2024/events
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4. https://cottonbureau.com/people/advent-of-code
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5. https://adventofcode.com/2024/settings
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6. https://adventofcode.com/2024/auth/logout
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7. Advent of Code Supporter
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https://adventofcode.com/2024/support
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8. https://adventofcode.com/2024
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9. https://adventofcode.com/2024
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10. https://adventofcode.com/2024/support
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11. https://adventofcode.com/2024/sponsors
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12. https://adventofcode.com/2024/leaderboard
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13. https://adventofcode.com/2024/stats
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16. https://adventofcode.com/2023/day/12
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17. https://www.youtube.com/watch?v=ekL881PJMjI
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18. https://en.wikipedia.org/wiki/Onsen
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19. https://adventofcode.com/2024
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20. https://adventofcode.com/2024/day/19/input
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