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Square Your Age (Posted on 2003-04-15) Difficulty: 2 of 5
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?

See The Solution Submitted by pleasance    
Rating: 2.7500 (8 votes)

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re(2): Direct approach | Comment 12 of 20 |
(In reply to re: Direct approach by Ravi Raja)

The possibility of x=44 depends on "The other day" referring to a time before 1936, so that the future tense is warranted in Jim's statement. If someone were talking to me and said something about "the other day" and I later found out they were talking about something that happened that long ago, I would feel as if whoever said it was trying to deceive me.

Also, the possibility of x=44 would imply that pleasance was old enough in 1936 to understand perfect squares. And I thought that I was one of the older flooblers and even I wasn't yet born in 1936.

As a probability problem I'd put P(x=44) << .01, where << means is much less than.
  Posted by Charlie on 2003-04-16 05:29:07

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