90 lines
4.3 KiB
Markdown
90 lines
4.3 KiB
Markdown
--- Day 6: Wait For It ---
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The ferry quickly brings you across Island Island. After asking around, you
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discover that there is indeed normally a large pile of sand somewhere near here,
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but you don't see anything besides lots of water and the small island where the
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ferry has docked.
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As you try to figure out what to do next, you notice a poster on a wall near the
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ferry dock. "Boat races! Open to the public! Grand prize is an all-expenses-paid
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trip to Desert Island!" That must be where the sand comes from! Best of all, the
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boat races are starting in just a few minutes.
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You manage to sign up as a competitor in the boat races just in time. The
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organizer explains that it's not really a traditional race - instead, you will
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get a fixed amount of time during which your boat has to travel as far as it
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can, and you win if your boat goes the farthest.
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As part of signing up, you get a sheet of paper (your puzzle input) that lists
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the time allowed for each race and also the best distance ever recorded in that
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race. To guarantee you win the grand prize, you need to make sure you go farther
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in each race than the current record holder.
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The organizer brings you over to the area where the boat races are held. The
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boats are much smaller than you expected - they're actually toy boats, each with
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a big button on top. Holding down the button charges the boat, and releasing the
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button allows the boat to move. Boats move faster if their button was held
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longer, but time spent holding the button counts against the total race time.
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You can only hold the button at the start of the race, and boats don't move
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until the button is released.
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For example:
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```
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Time: 7 15 30
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Distance: 9 40 200
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```
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This document describes three races:
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- The first race lasts 7 milliseconds. The record distance in this race is 9
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millimeters.
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- The second race lasts 15 milliseconds. The record distance in this race is 40
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millimeters.
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- The third race lasts 30 milliseconds. The record distance in this race is 200
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millimeters.
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Your toy boat has a starting speed of zero millimeters per millisecond. For each
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whole millisecond you spend at the beginning of the race holding down the
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button, the boat's speed increases by one millimeter per millisecond.
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So, because the first race lasts 7 milliseconds, you only have a few options:
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- Don't hold the button at all (that is, hold it for 0 milliseconds) at the
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start of the race. The boat won't move; it will have traveled 0 millimeters by
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the end of the race.
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- Hold the button for 1 millisecond at the start of the race. Then, the boat
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will travel at a speed of 1 millimeter per millisecond for 6 milliseconds,
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reaching a total distance traveled of 6 millimeters.
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- Hold the button for 2 milliseconds, giving the boat a speed of 2 millimeters
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per millisecond. It will then get 5 milliseconds to move, reaching a total
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distance of 10 millimeters.
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- Hold the button for 3 milliseconds. After its remaining 4 milliseconds of
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travel time, the boat will have gone 12 millimeters.
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- Hold the button for 4 milliseconds. After its remaining 3 milliseconds of
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travel time, the boat will have gone 12 millimeters.
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- Hold the button for 5 milliseconds, causing the boat to travel a total of 10
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millimeters.
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- Hold the button for 6 milliseconds, causing the boat to travel a total of 6
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millimeters.
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- Hold the button for 7 milliseconds. That's the entire duration of the race.
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You never let go of the button. The boat can't move until you let go of the
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button. Please make sure you let go of the button so the boat gets to move. 0
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millimeters. Since the current record for this race is 9 millimeters, there
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are actually 4 different ways you could win: you could hold the button for 2,
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3, 4, or 5 milliseconds at the start of the race.
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In the second race, you could hold the button for at least 4 milliseconds and at
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most 11 milliseconds and beat the record, a total of 8 different ways to win.
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In the third race, you could hold the button for at least 11 milliseconds and no
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more than 19 milliseconds and still beat the record, a total of 9 ways you could
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win.
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To see how much margin of error you have, determine the number of ways you can
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beat the record in each race; in this example, if you multiply these values
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together, you get 288 (4 * 8 * 9).
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Determine the number of ways you could beat the record in each race. What do you
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get if you multiply these numbers together?
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