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?

√1871=43.255... We want a date before 1871, so go with x=43 and born 43²-43=1806 for De Morgan.

"The other day" implies recency, and the speaking is for the future, so calculate √2002 = 44.74... As it's in the future, round up to x=45 and the year of birth is 45²-45=1980 for Jim.

Posted by Charlie on 2003-04-16 04:57:34