2023 - Day 6

2023/06/PART1.md

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