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 know that De Morgan's age was between 41 and 44, assuming that there even is a solution. Let's finish by listing all the squares in this range
41^2 = 1681,
42^2 = 1764,
43^2 = 1849,
44^2 = 1936.
So, the only possible age, consistent with the given information and our assumption of the age of De Morgan when he died, is 43 years old. he was born when the year was 1849. So the answer is x = 43.
the only resonable answer i can think of for jim is that he was born in 1980 and will be 45 in 2025.
am i off here?
guess
