Question
If 19 August 2001 is a Sunday, then what will be the day
of the week on 15 May 2010?Solution
Quick check:
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Remaining days in 2001 after Aug 19: 12+30+31+30+31=13412+30+31+30+31=134 12 + 30 + 31 + 30 + 31 = 134
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Full years 2002–2009: 8×365+28\times365+2 8 × 365 + 2 leap days =2922=2922 = 2922
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Days in 2010 up to May 15: 31+28+31+30+15=13531+28+31+30+15=135 31 + 28 + 31 + 30 + 15 = 135
Total =134+2922+135=3191=134+2922+135=3191 = 134 + 2922 + 135 = 3191 .
3191 mod 7=63191 \bmod 7 = 6 3191 mod 7 = 6 . From Sunday, +6 days ⇒ Saturday .
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