237 lines
9.1 KiB
Plaintext
237 lines
9.1 KiB
Plaintext
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Advent of Code
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--- Day 22: Monkey Market ---
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As you're all teleported deep into the jungle, a [16]monkey steals The
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Historians' device! You'll need to get it back while The Historians are
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looking for the Chief.
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The monkey that stole the device seems willing to trade it, but only in
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exchange for an absurd number of bananas. Your only option is to buy
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bananas on the Monkey Exchange Market.
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You aren't sure how the Monkey Exchange Market works, but one of The
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Historians senses trouble and comes over to help. Apparently, they've been
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studying these monkeys for a while and have deciphered their secrets.
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Today, the Market is full of monkeys buying good hiding spots.
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Fortunately, because of the time you recently spent in this jungle, you
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know lots of good hiding spots you can sell! If you sell enough hiding
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spots, you should be able to get enough bananas to buy the device back.
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On the Market, the buyers seem to use random prices, but their prices are
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actually only [17]pseudorandom! If you know the secret of how they pick
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their prices, you can wait for the perfect time to sell.
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The part about secrets is literal, the Historian explains. Each buyer
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produces a pseudorandom sequence of secret numbers where each secret is
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derived from the previous.
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In particular, each buyer's secret number evolves into the next secret
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number in the sequence via the following process:
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• Calculate the result of multiplying the secret number by 64. Then, mix
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this result into the secret number. Finally, prune the secret number.
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• Calculate the result of dividing the secret number by 32. Round the
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result down to the nearest integer. Then, mix this result into the
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secret number. Finally, prune the secret number.
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• Calculate the result of multiplying the secret number by 2048. Then,
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mix this result into the secret number. Finally, prune the secret
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number.
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Each step of the above process involves mixing and pruning:
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• To mix a value into the secret number, calculate the [18]bitwise XOR
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of the given value and the secret number. Then, the secret number
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becomes the result of that operation. (If the secret number is 42 and
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you were to mix 15 into the secret number, the secret number would
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become 37.)
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• To prune the secret number, calculate the value of the secret number
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[19]modulo 16777216. Then, the secret number becomes the result of
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that operation. (If the secret number is 100000000 and you were to
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prune the secret number, the secret number would become 16113920.)
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After this process completes, the buyer is left with the next secret
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number in the sequence. The buyer can repeat this process as many times as
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necessary to produce more secret numbers.
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So, if a buyer had a secret number of 123, that buyer's next ten secret
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numbers would be:
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15887950
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16495136
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527345
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704524
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1553684
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12683156
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11100544
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12249484
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7753432
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5908254
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Each buyer uses their own secret number when choosing their price, so it's
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important to be able to predict the sequence of secret numbers for each
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buyer. Fortunately, the Historian's research has uncovered the initial
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secret number of each buyer (your puzzle input). For example:
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1
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10
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100
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2024
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This list describes the initial secret number of four different
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secret-hiding-spot-buyers on the Monkey Exchange Market. If you can
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simulate secret numbers from each buyer, you'll be able to predict all of
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their future prices.
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In a single day, buyers each have time to generate 2000 new secret
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numbers. In this example, for each buyer, their initial secret number and
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the 2000th new secret number they would generate are:
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1: 8685429
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10: 4700978
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100: 15273692
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2024: 8667524
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Adding up the 2000th new secret number for each buyer produces 37327623.
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For each buyer, simulate the creation of 2000 new secret numbers. What is
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the sum of the 2000th secret number generated by each buyer?
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Your puzzle answer was 14082561342.
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--- Part Two ---
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Of course, the secret numbers aren't the prices each buyer is offering!
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That would be ridiculous. Instead, the prices the buyer offers are just
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the ones digit of each of their secret numbers.
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So, if a buyer starts with a secret number of 123, that buyer's first ten
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prices would be:
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3 (from 123)
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0 (from 15887950)
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6 (from 16495136)
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5 (etc.)
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4
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4
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6
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4
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4
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2
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This price is the number of bananas that buyer is offering in exchange for
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your information about a new hiding spot. However, you still don't speak
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[20]monkey, so you can't negotiate with the buyers directly. The Historian
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speaks a little, but not enough to negotiate; instead, he can ask another
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monkey to negotiate on your behalf.
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Unfortunately, the monkey only knows how to decide when to sell by looking
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at the changes in price. Specifically, the monkey will only look for a
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specific sequence of four consecutive changes in price, then immediately
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sell when it sees that sequence.
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So, if a buyer starts with a secret number of 123, that buyer's first ten
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secret numbers, prices, and the associated changes would be:
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123: 3
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15887950: 0 (-3)
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16495136: 6 (6)
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527345: 5 (-1)
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704524: 4 (-1)
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1553684: 4 (0)
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12683156: 6 (2)
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11100544: 4 (-2)
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12249484: 4 (0)
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7753432: 2 (-2)
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Note that the first price has no associated change because there was no
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previous price to compare it with.
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In this short example, within just these first few prices, the highest
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price will be 6, so it would be nice to give the monkey instructions that
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would make it sell at that time. The first 6 occurs after only two
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changes, so there's no way to instruct the monkey to sell then, but the
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second 6 occurs after the changes -1,-1,0,2. So, if you gave the monkey
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that sequence of changes, it would wait until the first time it sees that
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sequence and then immediately sell your hiding spot information at the
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current price, winning you 6 bananas.
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Each buyer only wants to buy one hiding spot, so after the hiding spot is
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sold, the monkey will move on to the next buyer. If the monkey never hears
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that sequence of price changes from a buyer, the monkey will never sell,
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and will instead just move on to the next buyer.
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Worse, you can only give the monkey a single sequence of four price
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changes to look for. You can't change the sequence between buyers.
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You're going to need as many bananas as possible, so you'll need to
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determine which sequence of four price changes will cause the monkey to
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get you the most bananas overall. Each buyer is going to generate 2000
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secret numbers after their initial secret number, so, for each buyer,
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you'll have 2000 price changes in which your sequence can occur.
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Suppose the initial secret number of each buyer is:
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1
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2
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3
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2024
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There are many sequences of four price changes you could tell the monkey,
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but for these four buyers, the sequence that will get you the most bananas
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is -2,1,-1,3. Using that sequence, the monkey will make the following
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sales:
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• For the buyer with an initial secret number of 1, changes -2,1,-1,3
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first occur when the price is 7.
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• For the buyer with initial secret 2, changes -2,1,-1,3 first occur
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when the price is 7.
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• For the buyer with initial secret 3, the change sequence -2,1,-1,3
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does not occur in the first 2000 changes.
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• For the buyer starting with 2024, changes -2,1,-1,3 first occur when
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the price is 9.
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So, by asking the monkey to sell the first time each buyer's prices go
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down 2, then up 1, then down 1, then up 3, you would get 23 (7 + 7 + 9)
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bananas!
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Figure out the best sequence to tell the monkey so that by looking for
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that same sequence of changes in every buyer's future prices, you get the
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most bananas in total. What is the most bananas you can get?
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Your puzzle answer was 1568.
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Both parts of this puzzle are complete! They provide two gold stars: **
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At this point, you should [21]return to your Advent calendar and try
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another puzzle.
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If you still want to see it, you can [22]get your puzzle input.
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References
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Visible links
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1. https://adventofcode.com/
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2. https://adventofcode.com/2024/about
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3. https://adventofcode.com/2024/events
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4. https://cottonbureau.com/people/advent-of-code
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5. https://adventofcode.com/2024/settings
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6. https://adventofcode.com/2024/auth/logout
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7. Advent of Code Supporter
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https://adventofcode.com/2024/support
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8. https://adventofcode.com/2024
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9. https://adventofcode.com/2024
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10. https://adventofcode.com/2024/support
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11. https://adventofcode.com/2024/sponsors
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12. https://adventofcode.com/2024/leaderboard
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13. https://adventofcode.com/2024/stats
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14. https://adventofcode.com/2024/sponsors
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16. https://adventofcode.com/2022/day/11
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17. https://en.wikipedia.org/wiki/Pseudorandom_number_generator
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18. https://en.wikipedia.org/wiki/Bitwise_operation#XOR
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19. https://en.wikipedia.org/wiki/Modulo
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20. https://adventofcode.com/2022/day/21
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21. https://adventofcode.com/2024
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22. https://adventofcode.com/2024/day/22/input
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