If 19 July 2000 was a Wednesday, then what would be the day of the week on 15 June 2012?
Friday
Step 1 – Odd days from 19 July 2000 to 19 July 2012:
This 12-year span crosses three leap-year Februaries (2004, 2008, 2012) and nine ordinary years.
Total odd days = \(9\times 1 + 3\times 2 = 15 \equiv 1 \pmod 7\).
So 19 July 2012 = Wednesday + 1 = Thursday.
Step 2 – Roll back from 19 July 2012 to 15 June 2012:
Day difference = 34; odd days = \(34 \bmod 7 = 6\).
15 June 2012 = Thursday − 6 = Friday.
Hence, 15 June 2012 was a Friday.
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