Ganesh, the grandson of Mahesh, was born on his grandfather's birthday. Once, when the family was celebrating their birthdays (including Ganesh's father), the grandson told Mahesh that not only had he just turned as old as the last two digits of the year he was born in, but also his age was a prime number and each of the two digits making up his age were also prime. The grandson was surprised when Mahesh turned to him and said that each of the two digits making up his age was identical to that of his grandson's age. This may have occurred in which of the following years?

Ganesh's age must be a prime number where both digits are prime, meaning the only possible ages are 23, 37, or 53. The grandfather shares the exact same digits in his age, making the possible grandfather ages 32, 73, or 35. We test the year 1937 by checking Ganesh's birth year (1937 minus 37 equals 1900), revealing the grandfather's birth year is 1937 minus 73, which is 1864. Since a man born in 1864 turning 73 in 1937 while his grandson born in 1900 turns 37 is logically sound, the event occurred in 1937.

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