89 lines
2.4 KiB
Markdown
89 lines
2.4 KiB
Markdown
# Saturnalia's Problem
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**Kronos** is the father of the Olympian gods, and is the king of the Titans. He is the Titan god of
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Time, Justice, and Evil.
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After the Olympians defeated the titans, Kronos was given a new fate: he now rules over the Isles of
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the Blessed and the region of Latium near the Roman Empire. Next month, the festival **Saturnalia**.
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You've been given the task to schedule and organize the arrival of the citizens of Isles of the
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Blessed and Latium to reach Mount Othrys by ship.
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Unfortunately, there are far too many ships to calculate this all by hand. Each ship takes a
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different amount of time to return back to Mount Othrys, and you need to make sure everyone arrives
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at the same time.
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You have been given the shipping planner, that tells you how long it takes for each ship to reach
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either Isles of the Blessed or Latium, in minutes, and return back.
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Each ship initially departs at the same time, and continues to do as many rounds as needed, such
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that **each ship returns back to Mount Othrys at the same time**.
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Your task is to determine for the given ships, what is the fewest number of minutes until each ship
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returns back at the same time after the leave?
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### Example
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- Given the following input
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```
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3
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5
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9
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```
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Says that there are 3 different ships. The first one takes `3` minutes to complete a cycle, the
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second takes `5`, and `9` minutes for last ship. After `45` minutes, all of them will return back
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to Mount Othrys **at the same time**.
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- Given the following input
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```
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3
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12
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15
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9
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5
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73
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19
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49
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10
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13
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```
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Says that there are a total of 10 ships, and all of them will return back after `159,033,420`
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minutes.
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**How many minutes** will your ships take to all return back at the same time?
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Hint: The numbers might get a bit large here!
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{{ if eq .Part 2 }}
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**Congratulations! You got Part 1 correct. Your answer was `{{ .Answer1 }}`.**
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## Part 2
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To continue planning for the journey, Kronos needs figure out what the total number of journeys will
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be for each ship, summed all together.
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### Example
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Given the following input:
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```
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3
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5
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9
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```
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The total duration will still be `45` minutes before all the ships return again to the same
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position. In this time, the first ship will complete `15` trips, the second ship will complete `9`
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trips, and the last ship will complete `5` trips, for a total of `29` trips.
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With these new instructions, **how many steps total trips will all the ships complete?**
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{{ end }}
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