Question 8 — A total of 37 - Questions at the end of the chapter - Chapter 11 Class 8 - Keeping Time with the Skies (Curiosity)

Last updated at June 17, 2026 by

Q 8
Question

A total of 37 full Moons happen during 3 years in a solar calendar. Show that at least two of the 37 full moons must happen during the same month of the solar calendar.

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Answer
37 full Moons into 36 month-slots forces a repeat.

Explanation

  • Three years have 3 × 12 = 36 calendar months.
  • There are 37 full Moons to fit into these 36 months.
  • If each month had at most one full Moon, only 36 could fit.
  • Since there are 37, at least one month must contain two full Moons.
With 37 full Moons but only 36 months in three years, at least two full Moons must share the same month.
← Back to concept: 11.2 How Did Calendars Come into Existence?
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