2022: init day 10
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2022/day10/README.org
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2022/day10/README.org
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** --- Day 10: Cathode-Ray Tube ---
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You avoid the ropes, plunge into the river, and swim to shore.
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The Elves yell something about meeting back up with them upriver, but
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the river is too loud to tell exactly what they're saying. They finish
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crossing the bridge and disappear from view.
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Situations like this must be why the Elves prioritized getting the
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communication system on your handheld device working. You pull it out of
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your pack, but the amount of water slowly draining from a big crack in
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its screen tells you it probably won't be of much immediate use.
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/Unless/, that is, you can design a replacement for the device's video
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system! It seems to be some kind of
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[[https://en.wikipedia.org/wiki/Cathode-ray_tube][cathode-ray tube]]
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screen and simple CPU that are both driven by a precise /clock circuit/.
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The clock circuit ticks at a constant rate; each tick is called a
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/cycle/.
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Start by figuring out the signal being sent by the CPU. The CPU has a
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single register, =X=, which starts with the value =1=. It supports only
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two instructions:
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- =addx V= takes /two cycles/ to complete. /After/ two cycles, the =X=
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register is increased by the value =V=. (=V= can be negative.)
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- =noop= takes /one cycle/ to complete. It has no other effect.
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The CPU uses these instructions in a program (your puzzle input) to,
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somehow, tell the screen what to draw.
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Consider the following small program:
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#+begin_example
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noop
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addx 3
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addx -5
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#+end_example
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Execution of this program proceeds as follows:
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- At the start of the first cycle, the =noop= instruction begins
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execution. During the first cycle, =X= is =1=. After the first cycle,
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the =noop= instruction finishes execution, doing nothing.
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- At the start of the second cycle, the =addx 3= instruction begins
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execution. During the second cycle, =X= is still =1=.
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- During the third cycle, =X= is still =1=. After the third cycle, the
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=addx 3= instruction finishes execution, setting =X= to =4=.
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- At the start of the fourth cycle, the =addx -5= instruction begins
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execution. During the fourth cycle, =X= is still =4=.
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- During the fifth cycle, =X= is still =4=. After the fifth cycle, the
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=addx -5= instruction finishes execution, setting =X= to =-1=.
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Maybe you can learn something by looking at the value of the =X=
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register throughout execution. For now, consider the /signal strength/
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(the cycle number multiplied by the value of the =X= register) /during/
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the 20th cycle and every 40 cycles after that (that is, during the 20th,
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60th, 100th, 140th, 180th, and 220th cycles).
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For example, consider this larger program:
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#+begin_example
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addx 15
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addx -11
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addx 6
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addx -3
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addx 5
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addx -1
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addx -8
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addx 13
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addx 4
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noop
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addx -1
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addx 5
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addx -1
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addx 5
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addx -1
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addx 5
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addx -1
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addx 5
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addx -1
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addx -35
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addx 1
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addx 24
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addx -19
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addx 1
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addx 16
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addx -11
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noop
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noop
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addx 21
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addx -15
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noop
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noop
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addx -3
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addx 9
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addx 1
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addx -3
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addx 8
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addx 1
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addx 5
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noop
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noop
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noop
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noop
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noop
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addx -36
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noop
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addx 1
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addx 7
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noop
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noop
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noop
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addx 2
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addx 6
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noop
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noop
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noop
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noop
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noop
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addx 1
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noop
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noop
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addx 7
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addx 1
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noop
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addx -13
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addx 13
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addx 7
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noop
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addx 1
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addx -33
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noop
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noop
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noop
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addx 2
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noop
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noop
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noop
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addx 8
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noop
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addx -1
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addx 2
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addx 1
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noop
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addx 17
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addx -9
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addx 1
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addx 1
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addx -3
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addx 11
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noop
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noop
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addx 1
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noop
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addx 1
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noop
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noop
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addx -13
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addx -19
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addx 1
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addx 3
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addx 26
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addx -30
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addx 12
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addx -1
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addx 3
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addx 1
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noop
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noop
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noop
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addx -9
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addx 18
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addx 1
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addx 2
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noop
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noop
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addx 9
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noop
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noop
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noop
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addx -1
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addx 2
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addx -37
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addx 1
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addx 3
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noop
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addx 15
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addx -21
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addx 22
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addx -6
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addx 1
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noop
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addx 2
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addx 1
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noop
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addx -10
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noop
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noop
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addx 20
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addx 1
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addx 2
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addx 2
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addx -6
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addx -11
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noop
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noop
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noop
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#+end_example
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The interesting signal strengths can be determined as follows:
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- During the 20th cycle, register =X= has the value =21=, so the signal
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strength is 20 * 21 = /420/. (The 20th cycle occurs in the middle of
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the second =addx -1=, so the value of register =X= is the starting
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value, =1=, plus all of the other =addx= values up to that point: 1 +
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15 - 11 + 6 - 3 + 5 - 1 - 8 + 13 + 4 = 21.)
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- During the 60th cycle, register =X= has the value =19=, so the signal
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strength is 60 * 19 = =1140=.
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- During the 100th cycle, register =X= has the value =18=, so the signal
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strength is 100 * 18 = =1800=.
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- During the 140th cycle, register =X= has the value =21=, so the signal
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strength is 140 * 21 = =2940=.
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- During the 180th cycle, register =X= has the value =16=, so the signal
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strength is 180 * 16 = =2880=.
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- During the 220th cycle, register =X= has the value =18=, so the signal
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strength is 220 * 18 = =3960=.
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The sum of these signal strengths is =13140=.
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Find the signal strength during the 20th, 60th, 100th, 140th, 180th, and
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220th cycles. /What is the sum of these six signal strengths?/
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