65 lines
2.9 KiB
Text
65 lines
2.9 KiB
Text
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You watch the Elves and their sleigh fade into the distance as they head toward the North Pole.
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Actually, you're the one fading. The falling sensation returns.
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The low fuel warning light is illuminated on your wrist-mounted device. Tapping it once causes it to project a hologram of the situation: a *300x300* grid of fuel cells and their current power levels, some negative. You're not sure what negative power means in the context of time travel, but it can't be good.
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Each fuel cell has a coordinate ranging *from 1 to 300* in both the X (horizontal) and Y (vertical) direction. In `X,Y` notation, the top-left cell is `1,1`, and the top-right cell is `300,1`.
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The interface lets you select *any 3x3 square* of fuel cells. To increase your chances of getting to your destination, you decide to choose the 3x3 square with the *largest total power*.
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The power level in a given fuel cell can be found through the following process:
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* Find the fuel cell's *rack ID*, which is its *X coordinate plus 10*.
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* Begin with a power level of the *rack ID* times the *Y coordinate*.
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* Increase the power level by the value of the *grid serial number* (your puzzle input).
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* Set the power level to itself multiplied by the *rack ID*.
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* Keep only the *hundreds digit* of the power level (so `12*3*45` becomes `3`; numbers with no hundreds digit become `0`).
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* *Subtract 5* from the power level.
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For example, to find the power level of the fuel cell at `3,5` in a grid with serial number `8`:
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* The rack ID is `3 + 10 = *13*`.
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* The power level starts at `13 * 5 = *65*`.
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* Adding the serial number produces `65 + 8 = *73*`.
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* Multiplying by the rack ID produces `73 * 13 = *949*`.
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* The hundreds digit of `*9*49` is `*9*`.
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* Subtracting 5 produces `9 - 5 = *4*`.
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So, the power level of this fuel cell is `*4*`.
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Here are some more example power levels:
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* Fuel cell at `122,79`, grid serial number `57`: power level `-5`.
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* Fuel cell at `217,196`, grid serial number `39`: power level `0`.
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* Fuel cell at `101,153`, grid serial number `71`: power level `4`.
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Your goal is to find the 3x3 square which has the largest total power. The square must be entirely within the 300x300 grid. Identify this square using the `X,Y` coordinate of its *top-left fuel cell*. For example:
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For grid serial number `18`, the largest total 3x3 square has a top-left corner of `*33,45*` (with a total power of `29`); these fuel cells appear in the middle of this 5x5 region:
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```
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-2 -4 4 4 4
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-4 4 4 4 -5
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4 3 3 4 -4
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1 1 2 4 -3
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-1 0 2 -5 -2
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```
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For grid serial number `42`, the largest 3x3 square's top-left is `*21,61*` (with a total power of `30`); they are in the middle of this region:
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```
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-3 4 2 2 2
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-4 4 3 3 4
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-5 3 3 4 -4
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4 3 3 4 -3
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3 3 3 -5 -1
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```
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*What is the `X,Y` coordinate of the top-left fuel cell of the 3x3 square with the largest total power?*
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Your puzzle input is `2187`.
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Answer:
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