35 lines
1.6 KiB
Plaintext
35 lines
1.6 KiB
Plaintext
--- Part Two ---
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The Elf says they've stopped producing snow because they aren't getting any
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water! He isn't sure why the water stopped; however, he can show you how to get
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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
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played, what is the fewest number of cubes of each color that could have been in
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the bag to make the game possible?
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Again consider the example games from earlier:
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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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In game 1, the game could have been played with as few as 4 red, 2 green, and 6
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blue cubes. If any color had even one fewer cube, the game would have been
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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
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cubes multiplied together. The power of the minimum set of cubes in game 1 is
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48. In games 2-5 it was 12, 1560, 630, and 36, respectively. Adding up these
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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
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is the sum of the power of these sets?
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