Question

given that 300th day of a particular year Y is a Saturday and the 200th day year y+1 also a Saturday use modular arithmetic to explain why the 100th day of the year Y-1 falls on a monda

Answer 1

Answer : Monday

There are either 65 + 200 = 265 or 66 + 200 = 266 days between the first two dates depending
upon whether or not year Y is a leap year. Since 7 divides into 266, then it is possible for
both dates to Saturday ;

hence year Y+ 1 is a leap year and Y − 1 is not a leap year. There
are 265 + 300 = 565 days between the date in years Y, Y− 1, which leaves a remainder of
5 upon division by 7. Since we are subtracting days, we count 5 days before Saturday , which
gives us Monday.

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