How old?

[stealth]

Well, my problem on bugs didn't gain enough popularity as it seems, and so I decided to entertain you with an easier one, much easier. :)

 

Here is an innocent problem about aging:

 

A man born in the eighteenth century was [math]x[/math] years old in the year [math]x^2[/math]. How old was he in 1776? (Make no correction for calendric changes.) Is there a corresponding puzzle for the nineteenth century? If so, find the man's age in 1876. Show that there is no corresponding puzzle for the twentieth century.

[stealth]

Hey, guys! What's wrong? Is the problem trivial? What's the answer? :shrug:

[eric l]

For a corresponding puzzle in the 20th century, "a man aged x in the year x²" would indeed have been born in the 19th century.

How to proceed ? Starting with 1701, we put down all the numbers that are the square of an entire number, together with that number. By substracting the latter from the former, we have the year of birth.

Here we go :

1764 - 42 = 1722

1849 - 43 = 1806

1936 - 44 = 1892

2025 - 45 = 1980

Going back to earlier centuries, we find :

1681 - 41 = 1640

1600 - 40 = 1560 (the year 1600 marks the end of the 16th century)

1521 - 39 = 1482 (different centuries again)

1444 - 38 = 1406

1369 - 37 = 1332

1296 - 36 = 1260

1225 - 35 = 1190 (different centuries)

1156 - 34 = 1122

1089 - 33 = 1056

1024 - 32 = 992

961 - 31 = 930

900 - 30 = 870 (the year 900 marks the end of the 9th century)

841 - 29 = 812

We could go on till year 1, but then our man would have been born in the year -1, as there is no uear 0, and again that would be a different century.

 

Calculating the age of our man in a given year is simply an other substraction - our man would have been 44 in 1776 or 70 in 1876, depending on the case.

 

Of course, proving it impossible wiht variables rather than with actual numbers is another matter. Paraphrasing Fermat I would say that it is to lenghty for this forum.

[Tormod]

Hey, guys! What's wrong? Is the problem trivial? What's the answer? :hihi:

 

Problems like these are usually posted in the Watercooler or the lounge, so maybe people aren't used to seeing them here.

[TheBigDog]

(53 and 54) or 54 or (54 and 55) depending upon what day of the year and what day is his birthday.

 

Bill

[stealth]

OK! Eric l, your solution is correct! You did even more than required! Good job! Though you made a minor mistake while subtracting - it must be 54 years old for the year 1776, not 44, but it doesn't matter. TheBigDog confirmed the fact. :)