102 lines
4.2 KiB
Plaintext
102 lines
4.2 KiB
Plaintext
Advent of Code
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--- Day 25: Let It Snow ---
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Merry Christmas! Santa is booting up his weather machine; looks like you
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might get a white Christmas after all.
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The weather machine beeps! On the console of the machine is a copy
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protection message asking you to enter a code from the instruction manual.
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Apparently, it refuses to run unless you give it that code. No problem;
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you'll just look up the code in the--
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"Ho ho ho", Santa ponders aloud. "I can't seem to find the manual."
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You look up the support number for the manufacturer and give them a call.
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Good thing, too - that 49th star wasn't going to earn itself.
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"Oh, that machine is quite old!", they tell you. "That model went out of
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support six minutes ago, and we just finished shredding all of the manuals.
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I bet we can find you the code generation algorithm, though."
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After putting you on hold for twenty minutes (your call is very important to
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them, it reminded you repeatedly), they finally find an engineer that
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remembers how the code system works.
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The codes are printed on an infinite sheet of paper, starting in the
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top-left corner. The codes are filled in by diagonals: starting with the
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first row with an empty first box, the codes are filled in diagonally up and
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to the right. This process repeats until the infinite paper is covered. So,
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the first few codes are filled in in this order:
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| 1 2 3 4 5 6
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---+---+---+---+---+---+---+
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1 | 1 3 6 10 15 21
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2 | 2 5 9 14 20
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3 | 4 8 13 19
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4 | 7 12 18
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5 | 11 17
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6 | 16
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For example, the 12th code would be written to row 4, column 2; the 15th
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code would be written to row 1, column 5.
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The voice on the other end of the phone continues with how the codes are
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actually generated. The first code is 20151125. After that, each code is
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generated by taking the previous one, multiplying it by 252533, and then
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keeping the remainder from dividing that value by 33554393.
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So, to find the second code (which ends up in row 2, column 1), start with
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the previous value, 20151125. Multiply it by 252533 to get 5088824049625.
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Then, divide that by 33554393, which leaves a remainder of 31916031. That
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remainder is the second code.
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"Oh!", says the voice. "It looks like we missed a scrap from one of the
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manuals. Let me read it to you." You write down his numbers:
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| 1 2 3 4 5 6
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---+---------+---------+---------+---------+---------+---------+
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1 | 20151125 18749137 17289845 30943339 10071777 33511524
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2 | 31916031 21629792 16929656 7726640 15514188 4041754
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3 | 16080970 8057251 1601130 7981243 11661866 16474243
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4 | 24592653 32451966 21345942 9380097 10600672 31527494
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5 | 77061 17552253 28094349 6899651 9250759 31663883
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6 | 33071741 6796745 25397450 24659492 1534922 27995004
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"Now remember", the voice continues, "that's not even all of the first few
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numbers; for example, you're missing the one at 7,1 that would come before
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6,2. But, it should be enough to let your-- oh, it's time for lunch! Bye!"
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The call disconnects.
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Santa looks nervous. Your puzzle input contains the message on the machine's
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console. What code do you give the machine?
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Your puzzle answer was 19980801.
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The first half of this puzzle is complete! It provides one gold star: *
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--- Part Two ---
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The machine springs to life, then falls silent again. It beeps.
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"Insufficient fuel", the console reads. "Fifty stars are required before
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proceeding. One star is available."
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..."one star is available"? You check the fuel tank; sure enough, a lone
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star sits at the bottom, awaiting its friends. Looks like you need to
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provide 49 yourself.
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You don't have enough stars to start the machine, though. You need x more.
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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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. http://adventofcode.com/day/1
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. https://en.wikipedia.org/wiki/Copy_protection#Early_video_games
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. https://en.wikipedia.org/wiki/Cantor's_diagonal_argument
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