Shikha celebrated her 32^nd birthday on Tuesday, 24^th January 2023. Which day of the week did she celebrate her 16^th birthday?

Given: Shikha celebrated her 32nd birthday on Tuesday, 24th January 2023.

Determine the year of Shikha's birth.

Shikha's birth year = Year of 32nd birthday - 32 years

Shikha's birth year = 2023 - 32 = 1991

Shikha was born on 24th January 1991.

Determine the year of Shikha's 16th birthday.

Year of 16th birthday = Birth year + 16 years

Year of 16th birthday = 1991 + 16 = 2007

Shikha's 16th birthday was on 24th January 2007.

Calculate the number of odd days between 24th January 2007 and 24th January 2023.

Number of years between 2007 and 2023 = 2023 - 2007 = 16 years.

Leap years between 2007 and 2023 are: 2008, 2012, 2016, 2020 (4 leap years).

Number of ordinary years = 16 - 4 = 12 years.

Number of odd days = (Number of ordinary years × 1) + (Number of leap years × 2)

Number of odd days = (12 × 1) + (4 × 2) = 12 + 8 = 20 odd days.

Determine the day of the week for Shikha's 16th birthday.

Day of 32nd birthday = Tuesday.

We need to go back 20 odd days from Tuesday.

20 odd days = 2 weeks and 6 odd days.

Going back 6 days from Tuesday is the same as going forward 1 day (since 6 backwards + 1 forwards = 7 days = 0 odd days).

Tuesday + 1 day = Wednesday.

Thus, Shikha celebrated her 16th birthday on Wednesday.

Hence, the correct answer is Wednesday.