77 lines
4.2 KiB
Markdown
77 lines
4.2 KiB
Markdown
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# Day 2: Cube Conundrum
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You're launched high into the atmosphere!
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The apex of your trajectory just barely reaches the surface of a large island floating in the sky.
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You gently land in a fluffy pile of leaves. It's quite cold, but you don't see much snow.
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An Elf runs over to greet you.
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The Elf explains that you've arrived at Snow Island and apologizes for the lack of snow.
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He'll be happy to explain the situation, but it's a bit of a walk, so you have some time.
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They don't get many visitors up here; would you like to play a game in the meantime?
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As you walk, the Elf shows you a small bag and some cubes which are either red, green, or blue.
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Each time you play this game, he will hide a secret number of cubes of each color in the bag,
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and your goal is to figure out information about the number of cubes.
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To get information, once a bag has been loaded with cubes, the Elf will reach into the bag,
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grab a handful of random cubes, show them to you, and then put them back in the bag.
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He'll do this a few times per game.
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You play several games and record the information from each game (your puzzle input).
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Each game is listed with its ID number (like the 11 in Game 11: ...) followed by a semicolon-separated list of subsets
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of cubes that were revealed from the bag (like 3 red, 5 green, 4 blue).
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For example, the record of a few games might look like this:
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```
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Game 1: 3 blue, 4 red; 1 red, 2 green, 6 blue; 2 green
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Game 2: 1 blue, 2 green; 3 green, 4 blue, 1 red; 1 green, 1 blue
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Game 3: 8 green, 6 blue, 20 red; 5 blue, 4 red, 13 green; 5 green, 1 red
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Game 4: 1 green, 3 red, 6 blue; 3 green, 6 red; 3 green, 15 blue, 14 red
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Game 5: 6 red, 1 blue, 3 green; 2 blue, 1 red, 2 green
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```
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In game 1, three sets of cubes are revealed from the bag (and then put back again).
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The first set is 3 blue cubes and 4 red cubes; the second set is 1 red cube, 2 green cubes, and 6 blue cubes;
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the third set is only 2 green cubes.
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The Elf would first like to know which games would have been possible if the bag contained only 12 red cubes,
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13 green cubes, and 14 blue cubes?
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In the example above, games 1, 2, and 5 would have been possible if the bag had been loaded with that configuration.
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However, game 3 would have been impossible because at one point the Elf showed you 20 red cubes at once; similarly,
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game 4 would also have been impossible because the Elf showed you 15 blue cubes at once.
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If you add up the IDs of the games that would have been possible, you get 8.
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Determine which games would have been possible if the bag had been loaded with only 12 red cubes, 13 green cubes,
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and 14 blue cubes. What is the sum of the IDs of those games?
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## Part Two
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The Elf says they've stopped producing snow because they aren't getting any water! He isn't sure why the water stopped;
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however, he can show you how to get to the water source to check it out for yourself. It's just up ahead!
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As you continue your walk, the Elf poses a second question: in each game you played,
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what is the fewest number of cubes of each color that could have been in the bag to make the game possible?
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Again consider the example games from earlier:
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```
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Game 1: 3 blue, 4 red; 1 red, 2 green, 6 blue; 2 green
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Game 2: 1 blue, 2 green; 3 green, 4 blue, 1 red; 1 green, 1 blue
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Game 3: 8 green, 6 blue, 20 red; 5 blue, 4 red, 13 green; 5 green, 1 red
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Game 4: 1 green, 3 red, 6 blue; 3 green, 6 red; 3 green, 15 blue, 14 red
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Game 5: 6 red, 1 blue, 3 green; 2 blue, 1 red, 2 green
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```
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- In game 1, the game could have been played with as few as 4 red, 2 green, and 6 blue cubes. If any color had even one fewer cube, the game would have been impossible.
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- Game 2 could have been played with a minimum of 1 red, 3 green, and 4 blue cubes.
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- Game 3 must have been played with at least 20 red, 13 green, and 6 blue cubes.
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- Game 4 required at least 14 red, 3 green, and 15 blue cubes.
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- Game 5 needed no fewer than 6 red, 3 green, and 2 blue cubes in the bag.
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The power of a set of cubes is equal to the numbers of red, green, and blue cubes multiplied together.
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The power of the minimum set of cubes in game 1 is 48. In games 2-5 it was 12, 1560, 630, and 36, respectively.
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Adding up these five powers produces the sum 2286.
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For each game, find the minimum set of cubes that must have been present. What is the sum of the power of these sets?
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