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Monday, November 2

Apprenticelogic & control flow

The Moonwarg Vigil of Pellacombe

Above the hill-village of Pellacombe hang two moons, pale Ilse and red Morrow. The Moonwarg pack of the Pellacombe barrows only leaves its dens on a night when both moons are full. The Wardens of Pellacombe are hiring hunters to lie in wait on that night, and they need to know which night it will be before their watch runs out.

Nights are numbered from 0 (tonight). Ilse is full on nights p, p + a, p + 2a, p + 3a, … and on no other night. Morrow is full on nights q, q + b, q + 2b, … and on no other night. No moon is full on any night before its first full night.

Write firstDoubleMoon(a, p, b, q, limit), where:

  • a and b are integers, each at least 1: the number of nights between consecutive full nights of Ilse and of Morrow.
  • p and q are integers, each at least 0: the first night on which Ilse and Morrow are full. They may be larger than a or b.
  • limit is an integer, at least 0: the last night of the Wardens' watch.

Return the smallest night n with 0 <= n <= limit on which both moons are full. If there is no such night within the watch, return -1. The bound is inclusive: a double full moon on night limit itself counts.

  • bounded search
  • Apprentice

examples

  1. case 1Ilse every 3 nights from night 1, Morrow every 4 nights from night 2, watch lasts to night 2010 (Ilse is full on 1, 4, 7, 10…; Morrow on 2, 6, 10…)
  2. case 2Ilse every 2 nights from night 9, Morrow every 3 nights from night 0, watch lasts to night 309 (night 3 does not count: Ilse is not yet full before night 9)
  3. case 3Ilse every 4 nights from night 1, Morrow every 6 nights from night 0, watch lasts to night 100-1 (Ilse is only full on odd nights, Morrow only on even ones)
reward
220 XP
signature
firstDoubleMoon
not yet run

TypeScript, run as ES2022 — types are stripped, not checked. If a JS engine would run it, so will we.

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  • basic coincidence
  • watch ends one night too early
  • coincidence exactly on the limit
  • both full tonight with zero-length watch
  • first full night larger than period
  • parities never meet
  • nightly moons with late starts
  • meet on later cycle
  • identical moons
  • identical moons watch ends before first full
  • larger periods
The Moonwarg Vigil of Pellacombe · bitwick