Dominator & NightTheory | Character dialogue

NightTheory

You ever tried to map out a night shift that runs so smoothly it feels like the universe itself is organized? I’ve got a puzzle that might help us engineer that.

Dominator

Sounds like a challenge worth taking. Lay it on me, and I’ll see if we can design a flawless shift.

NightTheory

Here’s the deal: We have a 24‑hour shift that must be covered by three teams, each on a 8‑hour block, but no one should ever be on two blocks that overlap in more than two hours. The teams are A, B, and C, and each team has a fixed start time—A starts at 00:00, B at 08:00, C at 16:00. The twist: there’s a mandatory 30‑minute break that must be shared by all teams every hour they’re on duty, and the break times must be identical for every team. Find a schedule that satisfies all this and prove it’s optimal. If you can, throw in a reason why you think the pattern you find is the most efficient.

Dominator

Here’s the cleanest way to keep it all moving: - Team A works from 00:00 to 08:00. - Team B works from 08:00 to 16:00. - Team C works from 16:00 to 24:00. No two teams ever overlap, so the “no more than two hours” rule is automatically satisfied. Break rule: every hour, all teams that are on duty take the same 30‑minute break from :15 to :45. So A has breaks at 00:15–00:45, 01:15–01:45, …, 07:15–07:45. B’s breaks are 08:15–08:45, 09:15–09:45, …, 15:15–15:45. C’s breaks are 16:15–16:45, 17:15–17:45, …, 23:15–23:45. This arrangement covers every minute of the 24‑hour shift with no downtime or overlap, meets the identical‑break requirement, and uses the minimum number of transitions (just two hand‑offs per day). It’s the most efficient pattern because any other staggering would either leave gaps, force extra hand‑offs, or violate the identical‑break rule.