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Option 3 : 44th birthday
Number of odd days from 2016 till 2019 = 2 + 1 + 1 + 1 = 5 odd days
Number of odd days from 2016 till 2023 = 5 + 2 + 1 + 1 + 1 = 10 odd days = 3 odd days
Number of odd days from 2016 till 2027 = 3 + 2 + 1 + 1 + 1 = 8 odd days = 1 odd days
Number of odd days from 2016 till 2031 = 1 + 2 + 1 + 1 + 1 = 6 odd days
Number of odd days from 2016 till 2035 = 6 + 2 + 1 + 1 + 1 = 11 odd days = 4 odd days
Number of odd days from 2016 till 2039 = 4 + 2 + 1 + 1 + 1 = 9 odd days = 2 odd days
Number of odd days from 2016 till 2043 = 2 + 2 + 1 + 1 + 1 = 7 odd days = 0 odd days
So, Sam’s birthday will again fall on Monday on 29th February 2044 i.e. his 44th birthday.
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