131 lines
4.7 KiB
Markdown
131 lines
4.7 KiB
Markdown
## \-\-- Day 13: Claw Contraption \-\--
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Next up: the [lobby](/2020/day/24) of a resort on a tropical island. The
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Historians take a moment to admire the hexagonal floor tiles before
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spreading out.
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Fortunately, it looks like the resort has a new
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[arcade](https://en.wikipedia.org/wiki/Amusement_arcade)! Maybe you can
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win some prizes from the [claw
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machines](https://en.wikipedia.org/wiki/Claw_machine)?
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The claw machines here are a little unusual. Instead of a joystick or
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directional buttons to control the claw, these machines have two buttons
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labeled `A` and `B`. Worse, you can\'t just put in a token and play; it
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costs *3 tokens* to push the `A` button and *1 token* to push the `B`
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button.
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With a little experimentation, you figure out that each machine\'s
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buttons are configured to move the claw a specific amount to the *right*
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(along the `X` axis) and a specific amount *forward* (along the `Y`
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axis) each time that button is pressed.
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Each machine contains one *prize*; to win the prize, the claw must be
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positioned *exactly* above the prize on both the `X` and `Y` axes.
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You wonder: what is the smallest number of tokens you would have to
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spend to win as many prizes as possible? You assemble a list of every
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machine\'s button behavior and prize location (your puzzle input). For
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example:
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Button A: X+94, Y+34
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Button B: X+22, Y+67
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Prize: X=8400, Y=5400
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Button A: X+26, Y+66
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Button B: X+67, Y+21
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Prize: X=12748, Y=12176
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Button A: X+17, Y+86
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Button B: X+84, Y+37
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Prize: X=7870, Y=6450
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Button A: X+69, Y+23
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Button B: X+27, Y+71
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Prize: X=18641, Y=10279
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This list describes the button configuration and prize location of four
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different claw machines.
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For now, consider just the first claw machine in the list:
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- Pushing the machine\'s `A` button would move the claw `94` units
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along the `X` axis and `34` units along the `Y` axis.
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- Pushing the `B` button would move the claw `22` units along the `X`
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axis and `67` units along the `Y` axis.
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- The prize is located at `X=8400`, `Y=5400`; this means that from the
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claw\'s initial position, it would need to move exactly `8400` units
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along the `X` axis and exactly `5400` units along the `Y` axis to be
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perfectly aligned with the prize in this machine.
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The cheapest way to win the prize is by pushing the `A` button `80`
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times and the `B` button `40` times. This would line up the claw along
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the `X` axis (because `80*94 + 40*22 = 8400`) and along the `Y` axis
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(because `80*34 + 40*67 = 5400`). Doing this would cost `80*3` tokens
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for the `A` presses and
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`40*1` for the `B` presses, a total of `280` tokens.
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For the second and fourth claw machines, there is no combination of A
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and B presses that will ever win a prize.
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For the third claw machine, the cheapest way to win the prize is by
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pushing the `A` button `38` times and the `B` button `86` times. Doing
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this would cost a total of `200` tokens.
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So, the most prizes you could possibly win is two; the minimum tokens
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you would have to spend to win all (two) prizes is `480`.
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You estimate that each button would need to be pressed *no more than
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`100` times* to win a prize. How else would someone be expected to play?
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Figure out how to win as many prizes as possible. *What is the fewest
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tokens you would have to spend to win all possible prizes?*
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Your puzzle answer was `30973`.
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## \-\-- Part Two \-\-- {#part2}
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As you go to win the first prize, you discover that the claw is nowhere
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near where you expected it would be. Due to a unit conversion error in
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your measurements, the position of every prize is actually
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`10000000000000` higher on both the `X` and `Y` axis!
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Add `10000000000000` to the `X` and `Y` position of every prize. After
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making this change, the example above would now look like this:
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Button A: X+94, Y+34
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Button B: X+22, Y+67
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Prize: X=10000000008400, Y=10000000005400
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Button A: X+26, Y+66
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Button B: X+67, Y+21
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Prize: X=10000000012748, Y=10000000012176
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Button A: X+17, Y+86
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Button B: X+84, Y+37
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Prize: X=10000000007870, Y=10000000006450
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Button A: X+69, Y+23
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Button B: X+27, Y+71
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Prize: X=10000000018641, Y=10000000010279
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Now, it is only possible to win a prize on the second and fourth claw
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machines. Unfortunately, it will take *many more than `100` presses* to
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do so.
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Using the corrected prize coordinates, figure out how to win as many
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prizes as possible. *What is the fewest tokens you would have to spend
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to win all possible prizes?*
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Your puzzle answer was `95688837203288`.
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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, you should [return to your Advent calendar](/2024) and
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try another puzzle.
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If you still want to see it, you can [get your puzzle
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input](13/input).
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