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| 1 | +# Day 6: Wait For It |
| 2 | +The ferry quickly brings you across Island Island. After asking around, you discover that there is indeed normally a |
| 3 | +large pile of sand somewhere near here, but you don't see anything besides lots of water and the small island where the |
| 4 | +ferry has docked. |
| 5 | + |
| 6 | +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 |
| 7 | +public! Grand prize is an all-expenses-paid trip to **Desert Island**!" That must be where the sand comes from! Best of |
| 8 | +all, the boat races are starting in just a few minutes. |
| 9 | + |
| 10 | +You manage to sign up as a competitor in the boat races just in time. The organizer explains that it's not really a |
| 11 | +traditional race - instead, you will get a fixed amount of time during which your boat has to travel as far as it can, |
| 12 | +and you win if your boat goes the farthest. |
| 13 | + |
| 14 | +As part of signing up, you get a sheet of paper (your puzzle input) that lists the **time** allowed for each race and |
| 15 | +also the best **distance** ever recorded in that race. To guarantee you win the grand prize, you need to make sure you |
| 16 | +**go farther in each race** than the current record holder. |
| 17 | + |
| 18 | +The organizer brings you over to the area where the boat races are held. The boats are much smaller than you expected - |
| 19 | +they're actually **toy boats**, each with a big button on top. Holding down the button **charges the boat**, and |
| 20 | +releasing the button **allows the boat to move**. Boats move faster if their button was held longer, but time spent |
| 21 | +holding the button counts against the total race time. You can only hold the button at the start of the race, and boats |
| 22 | +don't move until the button is released. |
| 23 | + |
| 24 | +For example: |
| 25 | +``` |
| 26 | +Time: 7 15 30 |
| 27 | +Distance: 9 40 200 |
| 28 | +``` |
| 29 | +This document describes three races: |
| 30 | +* The first race lasts `7` milliseconds. The record distance in this race is `9` millimeters. |
| 31 | +* The second race lasts `15` milliseconds. The record distance in this race is `40` millimeters. |
| 32 | +* The third race lasts `30` milliseconds. The record distance in this race is `200` millimeters. |
| 33 | + |
| 34 | +Your toy boat has a starting speed of **zero millimeters per millisecond**. For each whole millisecond you spend at the |
| 35 | +beginning of the race holding down the button, the boat's speed increases by **one millimeter per millisecond**. |
| 36 | + |
| 37 | +So, because the first race lasts `7` milliseconds, you only have a few options: |
| 38 | +* Don't hold the button at all (that is, hold it for **`0` milliseconds**) at the start of the race. The boat won't |
| 39 | +move; it will have traveled **`0` millimeters** by the end of the race. |
| 40 | +* Hold the button for **`1` millisecond** at the start of the race. Then, the boat will travel at a speed of `1` |
| 41 | +millimeter per millisecond for `6` milliseconds, reaching a total distance traveled of **`6` millimeters**. |
| 42 | +* Hold the button for **`2` milliseconds**, giving the boat a speed of `2` millimeters per millisecond. It will then |
| 43 | +get `5` milliseconds to move, reaching a total distance of **`10` millimeters**. |
| 44 | +* Hold the button for **`3` milliseconds**. After its remaining `4` milliseconds of travel time, the boat will have |
| 45 | +gone **`12` millimeters**. |
| 46 | +* Hold the button for **`4` milliseconds**. After its remaining `3` milliseconds of travel time, the boat will have |
| 47 | +gone **`12` millimeters**. |
| 48 | +* Hold the button for **`5` milliseconds**, causing the boat to travel a total of **`10` millimeters**. |
| 49 | +* Hold the button for **`6` milliseconds**, causing the boat to travel a total of **`6` millimeters**. |
| 50 | +* Hold the button for **`7` milliseconds**. That's the entire duration of the race. You never let go of the button. |
| 51 | +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 |
| 52 | +move. **`0` millimeters**. |
| 53 | + |
| 54 | +Since the current record for this race is `9` millimeters, there are actually **`4`** different ways you could win: |
| 55 | +you could hold the button for `2`, `3`, `4`, or `5` milliseconds at the start of the race. |
| 56 | + |
| 57 | +In the second race, you could hold the button for at least `4` milliseconds and at most `11` milliseconds and beat the |
| 58 | +record, a total of **`8`** different ways to win. |
| 59 | + |
| 60 | +In the third race, you could hold the button for at least `11` milliseconds and no more than `19` milliseconds and still |
| 61 | +beat the record, a total of **`9`** ways you could win. |
| 62 | + |
| 63 | +To see how much margin of error you have, determine the **number of ways you can beat the record** in each race; in |
| 64 | +this example, if you multiply these values together, you get **`288`** (`4` * `8` * `9`). |
| 65 | + |
| 66 | +Determine the number of ways you could beat the record in each race. **What do you get if you multiply these numbers |
| 67 | +together**? |
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