If 25 January 2018 is Thursday, what day will 25 June 2019 fall on?
Tuesday
For any calendar problem, count the number of odd days — the remainder when the total number of days between the two dates is divided by 7 — and advance the given weekday by that number.
Step 1 — From 25 January 2018 to 25 January 2019 is 365 days (2018 is not a leap year). \(365 \bmod 7 = 1\), so 25 Jan 2019 is one day after Thursday, i.e. Friday.
Step 2 — From 25 January 2019 to 25 June 2019, count month by month: Feb 28 + Mar 31 + Apr 30 + May 31 = 120 days from 25 Jan to 25 May, plus 31 more to 25 Jun gives 151. \(151 \bmod 7 = 4\), so 25 Jun 2019 is Friday + 4 days = Tuesday.
Step 3 — Cross-check with the direct total: from 25 Jan 2018 to 25 Jun 2019 is \(365 + 151 = 516\) days, and \(516 = 73 imes 7 + 5\), so there are 5 odd days. Thursday + 5 days = Tuesday, which agrees with Step 2.
Hence, Tuesday.
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