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Question Number 92687 by Ar Brandon last updated on 08/May/20

In a Gregorian calendar, a year finishing with  00 is a leap year if only it′s vintage is divisible  by 400. Also, the 1^(st)  January 1900 was a  Monday.  1\ Show that a year with the vintage finishing with  00 cannot begin on a Sunday  2\ Show that for a person born between 1900−2071,  his 28 anniversary will occur on the same  day of birth.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{Gregorian}\:\mathrm{calendar},\:\mathrm{a}\:\mathrm{year}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{is}\:\mathrm{a}\:\mathrm{leap}\:\mathrm{year}\:\mathrm{if}\:\mathrm{only}\:\mathrm{it}'\mathrm{s}\:\mathrm{vintage}\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{400}.\:\mathrm{Also},\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \:\mathrm{January}\:\mathrm{1900}\:\mathrm{was}\:\mathrm{a} \\ $$$$\mathrm{Monday}. \\ $$$$\mathrm{1}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{a}\:\mathrm{year}\:\mathrm{with}\:\mathrm{the}\:\mathrm{vintage}\:\mathrm{finishing}\:\mathrm{with} \\ $$$$\mathrm{00}\:\mathrm{cannot}\:\mathrm{begin}\:\mathrm{on}\:\mathrm{a}\:\mathrm{Sunday} \\ $$$$\mathrm{2}\backslash\:\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{a}\:\mathrm{person}\:\mathrm{born}\:\mathrm{between}\:\mathrm{1900}−\mathrm{2071}, \\ $$$$\mathrm{his}\:\mathrm{28}\:\mathrm{anniversary}\:\mathrm{will}\:\mathrm{occur}\:\mathrm{on}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{day}\:\mathrm{of}\:\mathrm{birth}. \\ $$

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