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

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

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