117 lines
5.2 KiB
Plaintext
117 lines
5.2 KiB
Plaintext
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Advent of Code
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br0xen 50*
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• [About]
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• [Stats]
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• [Leaderboard]
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• [Settings]
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• [Log out]
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--- Day 24: It Hangs in the Balance ---
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It's Christmas Eve, and Santa is loading up the sleigh for this year's deliveries. However,
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there's one small problem: he can't get the sleigh to balance. If it isn't balanced, he can't
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defy physics, and nobody gets presents this year.
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No pressure.
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Santa has provided you a list of the weights of every package he needs to fit on the sleigh.
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The packages need to be split into three groups of exactly the same weight, and every package
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has to fit. The first group goes in the passenger compartment of the sleigh, and the second
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and third go in containers on either side. Only when all three groups weigh exactly the same
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amount will the sleigh be able to fly. Defying physics has rules, you know!
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Of course, that's not the only problem. The first group - the one going in the passenger
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compartment - needs as few packages as possible so that Santa has some legroom left over. It
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doesn't matter how many packages are in either of the other two groups, so long as all of the
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groups weigh the same.
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Furthermore, Santa tells you, if there are multiple ways to arrange the packages such that the
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fewest possible are in the first group, you need to choose the way where the first group has
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the smallest quantum entanglement to reduce the chance of any "complications". The quantum
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entanglement of a group of packages is the product of their weights, that is, the value you
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get when you multiply their weights together. Only consider quantum entanglement if the first
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group has the fewest possible number of packages in it and all groups weigh the same amount.
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For example, suppose you have ten packages with weights 1 through 5 and 7 through 11. For this
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situation, some of the unique first groups, their quantum entanglements, and a way to divide
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the remaining packages are as follows:
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Group 1; Group 2; Group 3
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11 9 (QE= 99); 10 8 2; 7 5 4 3 1
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10 9 1 (QE= 90); 11 7 2; 8 5 4 3
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10 8 2 (QE=160); 11 9; 7 5 4 3 1
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10 7 3 (QE=210); 11 9; 8 5 4 2 1
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10 5 4 1 (QE=200); 11 9; 8 7 3 2
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10 5 3 2 (QE=300); 11 9; 8 7 4 1
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10 4 3 2 1 (QE=240); 11 9; 8 7 5
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9 8 3 (QE=216); 11 7 2; 10 5 4 1
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9 7 4 (QE=252); 11 8 1; 10 5 3 2
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9 5 4 2 (QE=360); 11 8 1; 10 7 3
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8 7 5 (QE=280); 11 9; 10 4 3 2 1
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8 5 4 3 (QE=480); 11 9; 10 7 2 1
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7 5 4 3 1 (QE=420); 11 9; 10 8 2
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Of these, although 10 9 1 has the smallest quantum entanglement (90), the configuration with
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only two packages, 11 9, in the passenger compartment gives Santa the most legroom and wins.
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In this situation, the quantum entanglement for the ideal configuration is therefore 99. Had
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there been two configurations with only two packages in the first group, the one with the
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smaller quantum entanglement would be chosen.
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What is the quantum entanglement of the first group of packages in the ideal configuration?
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Your puzzle answer was 10439961859.
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--- Part Two ---
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That's weird... the sleigh still isn't balancing.
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"Ho ho ho", Santa muses to himself. "I forgot the trunk".
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Balance the sleigh again, but this time, separate the packages into four groups instead of
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three. The other constraints still apply.
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Given the example packages above, this would be some of the new unique first groups, their
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quantum entanglements, and one way to divide the remaining packages:
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11 4 (QE=44); 10 5; 9 3 2 1; 8 7
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10 5 (QE=50); 11 4; 9 3 2 1; 8 7
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9 5 1 (QE=45); 11 4; 10 3 2; 8 7
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9 4 2 (QE=72); 11 3 1; 10 5; 8 7
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9 3 2 1 (QE=54); 11 4; 10 5; 8 7
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8 7 (QE=56); 11 4; 10 5; 9 3 2 1
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Of these, there are three arrangements that put the minimum (two) number of packages in the
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first group: 11 4, 10 5, and 8 7. Of these, 11 4 has the lowest quantum entanglement, and so
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it is selected.
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Now, what is the quantum entanglement of the first group of packages in the ideal
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configuration?
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Your puzzle answer was 72050269.
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Both parts of this puzzle are complete! They provide two gold stars: **
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At this point, all that is left is for you to admire your advent calendar.
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If you still want to see it, you can get your puzzle input.
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You can also [Shareon Twitter Google+ Reddit] this puzzle.
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References
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Visible links
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. http://adventofcode.com/
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. http://adventofcode.com/about
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. http://adventofcode.com/stats
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. http://adventofcode.com/leaderboard
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. http://adventofcode.com/settings
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. http://adventofcode.com/auth/logout
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. https://en.wikipedia.org/wiki/Product_%28mathematics%29
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. http://adventofcode.com/
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. http://adventofcode.com/day/24/input
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. https://twitter.com/intent/tweet?text=I%27ve+completed+%22It+Hangs+in+the+Balance%22+%2D+Day+24+%2D+Advent+of+Code&url=http%3A%2F%2Fadventofcode%2Ecom%2Fday%2F24&related=ericwastl&hashtags=AdventOfCode
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. https://plus.google.com/share?url=http%3A%2F%2Fadventofcode%2Ecom%2Fday%2F24
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. http://www.reddit.com/submit?url=http%3A%2F%2Fadventofcode%2Ecom%2Fday%2F24&title=I%27ve+completed+%22It+Hangs+in+the+Balance%22+%2D+Day+24+%2D+Advent+of+Code
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