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