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Cake day: September 9th, 2023

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  • You forgot doing the years, which is a bit trickier if we take into account the leap years.

    According to the Gregorian calendar, every fourth year is a leap year unless it’s divisible by 100 – except those divisible by 400 which are leap years anyway. Hence, the average length of one year (over 400 years) must be:

    365 + 1⁄4 − 1⁄100 + 1⁄400 = 365.2425 days

    So,

    1041 / 365.2425 ≈ 2.85 years

    Or 2 years and…

    0.850161194275 × 365.2425 ≈ 310 days and…

    0.514999999987 × 24 ≈ 12 hours and…

    0.359999999688 × 60 ≈ 21 minutes and…

    0.59999998128 × 60 ≈ 36 seconds

    1041 days is just about 2y 310d 12h 21m 36s

    Wtf, how did we go from 1041 whole days to fractions of a day? Damn leap years!

    Had we not been accounting for them, we would have had 2 years and…

    0.852054794521 × 365 = 311.000000000165 days

    Or simply 2y 311d if we just ignore that tiny rounding error or use fewer decimals.