Why do Christmas and New Year's Day always fall on the same day of the week? 25 ( mod 7) = 31 ( mod 7)O 7( mod 25) = 31 ( mod 7)O 7( mod 25) = 7( mod 31) 7( mod 7) = 31 ( mod 25)
Added by Nathan G.
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Step 1: A weekday repeats every 7 days because there are 7 days in a week; if two dates differ by a multiple of 7 days they fall on the same weekday. Show more…
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Matthew W.
Using arithmetic modulo 7 and information about some day, we can figure out what day of the week a specific date was. We know that October 19, 2020 is a Monday. What day of the week was January 1, 2020? To get to January 1, 2020, we must subtract the 31 days of January, 29 days of February, 31 days of March, 30 days of April, 31 days of May, 30 days 0f June, 31 days of July, 31 days of August, 30 days of September, 20 days of October, modulo 7: 31 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 18 = 292 ≡ 3 mod 7, which means that January 1, 2020 was 5 day before a Monday, so it was a Wednesday.
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