If 26th January, 2019 was a Saturday, what day of the week would it have been on the 15th of August, 2015?

Given: 26th January 2019 was a Saturday

Required: Day of the week on 15th August 2015

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To find the day, calculate the total number of days between 15th August 2015 and 26th January 2019.

Remaining days in August 2015 (after 15th): $31 - 15 = 16$ days

September 2015: $30$ days

October 2015: $31$ days

November 2015: $30$ days

December 2015: $31$ days

Days from August to December 2015: $16 + 30 + 31 + 30 + 31 = 138$ days

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Complete years:

Year 2016 (leap year): $366$ days

Year 2017: $365$ days

Year 2018: $365$ days

Total for complete years: $366 + 365 + 365 = 1096$ days

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January 2019 (up to 26th): $26$ days

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Total days from 15th August 2015 to 26th January 2019:

$138 + 1096 + 26 = 1260$ days

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To find the day of the week, calculate $1260 \mod 7$:

$1260 = 7 \times 180$

$1260 \mod 7 = 0$

Since the remainder is $0$, going back $1260$ days (exactly $180$ weeks) from Saturday gives Saturday.

Therefore, 15th August 2015 was a Saturday.

The answer is Option 1: Saturday.