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An approach

_{Statement As the question is of a grandfather and a grandson who live today, and both were born or have a special relationship in years that are perfect squares, we study perfect squares closer to our dates. In fact there are not many, since the square closest to 1900 is 1849 = 43 * 43, and a person born in that year, in 2010 would have nothing more and nothing less than 161 years. The next square is 1936 = 44 * 44, which is more likely, as a person born in the year 2010 would be 74 years (could be the grandfather). Then the square of 45 and is 2025. Obviously, This square can not be the date on which the grandfather was born. A person having in that year 45, have been born in 1980. The next square is much larger, and a person serving 46 years on that date (2116) not yet born. Therefore, the only possible solution to my cousin's birth in 1980, and therefore would have in 2010 30 years, and Grandpa must have been born in 1936 and have 74 years (or be a miracle of longevity and have more than 160 years .)}