# how old is he?

#### nanaseailie

Hi fellas,

I was given this puzzle in school. Here goes :

Jack's great-grandfather was a mathematician.

He was x years old on 26 june in the year x^2

How old was Jack's great-grandfather when he published his book, cosmic topology,

on 26 June in the year 1973?

my guess is x =44 and the answer to the question is 37

is it correct? I was doing trial and error using calc.

what is the smart / algebraic way of solving it?

#### skipjack

Forum Staff
The question is unclear... which person is being referred to as "he" in each of the places where "he" is used?

If anyone was born in the year xÂ² - x, where xÂ² - x < 1973, x is at most 44.

To conclude that x = 44, consider that if x were 43 or less, the year xÂ² - x would be the year 1806 or earlier.

#### weirddave

They way I'd find the answer is to take the integer of the root of 1973 to get a starting point for his age.
int((1973)^0.5) = 44
I'd then do the following:
43^2 = 1849, , born in (1849-43) 1806, he'd be 167 in 1973, not likely.
44^2 = 1936, born in (1936-44) 1892 he'd be 81 in 1973, quite possible!
45^2 = 2025, born in (2025-45) 1980, he hasn't been born yet in 1973
The last one isn't really required, since the answer will always be higher than the year that was initially rooted, but if time permits, a sanity check is always a good idea!
So I make it 81.

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