A man born in the first half of 19th century was X year old in year X square .when was he born.?
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He was born between 1800 and 1850 ,and the only square between these numbers is 1849,
So, the man is 43 years old in the year 1849( since,the man was x years old in year x square)
Therefore he was born in 1806(1849-43=1806)
hope it helps you...
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