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August 22nd, 2019, 10:21 PM   #1
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From: jakarta

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how old is he?

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?
nanaseailie is offline  
 
August 22nd, 2019, 11:16 PM   #2
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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 x² - x, where x² - x < 1973, x is at most 44.

To conclude that x = 44, consider that if x were 43 or less, the year x² - x would be the year 1806 or earlier.
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August 22nd, 2019, 11:28 PM   #3
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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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