117 lines
		
	
	
		
			5.2 KiB
		
	
	
	
		
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			117 lines
		
	
	
		
			5.2 KiB
		
	
	
	
		
			Plaintext
		
	
	
	
	
	
|                                            Advent of Code
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| 
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|    br0xen 50*
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| 
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|      • [About]
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|      • [Stats]
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|      • [Leaderboard]
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| 
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| --- Day 24: It Hangs in the Balance ---
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| 
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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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| 
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|    No pressure.
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| 
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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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| 
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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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| 
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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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| 
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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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| 
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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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| 
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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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| 
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|    What is the quantum entanglement of the first group of packages in the ideal configuration?
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| 
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|    Your puzzle answer was 10439961859.
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| 
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| --- Part Two ---
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| 
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|    That's weird... the sleigh still isn't balancing.
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| 
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|    "Ho ho ho", Santa muses to himself. "I forgot the trunk".
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| 
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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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| 
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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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| 
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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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| 
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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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| 
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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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| 
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|    Your puzzle answer was 72050269.
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| 
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|    Both parts of this puzzle are complete! They provide two gold stars: **
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| 
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|    At this point, all that is left is for you to admire your advent calendar.
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| 
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|    If you still want to see it, you can get your puzzle input.
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| 
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|    You can also [Shareon Twitter Google+ Reddit] this puzzle.
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| 
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| References
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