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?
(In reply to
re: Second Possibility by Gamer)
Gamer, this was what was stated in my comment " FIRST POSSIBILITY" : (Very Similar To Second Possibility)
We can calculate and see that:
(42)^2 = 1764, (43)^2 = 1849, (44)^2 = 1936 and (45)^2 = 2025.
So, it is obvious that Augustus De Morgan was 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.
Suppose "The other day...." as referred in the problem is SOMEDAY, say, in the year 2000 (arbitrarily chosen, and can be any year between 1980 and 2025), so that only in that interval he can say that he will be 'x' years in the year 'x^2', where x = 45. And in the year 2000, Jim would have been 20 years old and not 111. So could you please explain how did you get that ? I mean how can you say that Jim would have to be 111 years old for my second answer to be true ?
This case is similar to the "Second Possibility" Case which has also been discussed in one of my replies posted.
re(2): Second Possibility
