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The Following Formula Can Be Used to Find the Day

question 239

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The following formula can be used to find the day of the week on which a given year begins. First calculate a=y+(y1) /4(y1) /100+(y1) /400\mathrm { a } = \mathrm { y } + \llbracket ( \mathrm { y } - 1 ) / 4 \rrbracket - \llbracket ( \mathrm { y } - 1 ) / 100 \rrbracket + \llbracket ( \mathrm { y } - 1 ) / 400 \rrbracket where y represents the year and x\llbracket x \rrbracket represents the greatest integer less than or equal to xx . After finding aa , find the smallest nonnegative integer bb such that ab(mod7) a \equiv b ( \bmod 7 ) Then bb gives the day of January 1 , with b=0b = 0 representing Sunday, b=1b = 1 Monday and so on. Find the day of the week on which January 1 would occur in the year 1890 .


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