Lunar Phase State Lookup

Given the moon's state on day 1 of the year, plus a target `(season, day)`, return the moon state on that date. The moon cycles through 8 states with a period of 8 days. Requirements The moon has 8 distinct states cycling with period 8 days. Inputs: initial_state (the state on January 1 of the year), season, and day (together specifying a target date in the year). Return the moon's state on that target date. Seasons are treated as fixed month spans in the prompt (typical interpretation: spring = Mar-May, summer = Jun-Aug, fall = Sep-Nov, winter = Dec-Feb). Confirm the exact season-to-month mapping with the interviewer at the start. Notes Convert (season, day) to a day-of-year integer D (with D = 1 corresponding to Jan 1). The answer is states[(initial_index + D - 1) % 8], where states is the cycle order. The arithmetic is trivial; the round-tripping bug is the season-to-month mapping. The prompt is deliberately under-specified — clarify before coding. Watch leap years if the prompt specifies one; otherwise assume non-leap. Preparation Write a season_day_to_doy helper with explicit month boundaries as constants. Do not hardcode magic numbers inline. Verify with a single sanity test (initial = 'new moon', target = Jan 9, expected = 'new moon' again on the 9th day with 8-day period). If the season mapping is ambiguous during the live attempt, narrate the assumption and proceed — interviewers grade the clarification reflex.