The other day, Jim excitedly told me, "Did you realise I will turn x years old in the year x^2?"
He wasn't the first to think of this. The 19th century mathematician August de Morgan used to used to boast that he was x years old in the year x^2. He died in 1871.
In what year was Jim born? When will his prediction be true? In what year was de Morgan born? What is x in each case?
We can calculate and see that:
(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025.
So, it is obvious that 43 years old in the Year 1849, which implies that he was born in the year 1806, whereas Jim will turn 45 years in the year 2025 implying he was born in the year 1980.
So, in AUGUSTUS DE MORGAN's case, x = 43 and in JIM's case, x = 45. This was the first possibility.
First Possibility
