All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Father and son (Posted on 2008-08-04) Difficulty: 2 of 5
A man asks his father about his age.

Instead of giving a direct answer the father wrote down two positive integer numbers on a piece of paper and says:

- Sum these two numbers and evaluate the square root of the total. Doing this, youŽll get my age.

The son takes his pocket calculator and inadvertently types the two numbers, one after the other, without pressing the "+" button (e.g. if the numbers were 124 and 357, he types 124357, instead of the sum of the numbers).

After this he makes a second mistake by pressing the square root button, not once, but twice.

Finding an integer number as the result he shows it to his father:

- This is your age.

- No, youŽre wrong, but the number you found is precisely the age of your mother, who is older than me.

How old is the father?

Note: While a solution is trivial with the aid of a spreadsheet, can you derive it without one?

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
illiterate or innumerate? | Comment 1 of 11

If the father's integers are each three digits, then the only solution is if he is older than the mother.  Taking the fourth powers from 18 (104976) to 31 (923521), we find that the only solution is for 31 for the mother.  The father's age would then be the square root of 923+521=1444, i.e. 38.  Since he says "older than me" he is probably confused.

On reflection, I see that the integers do not have to be three digits (that was just an example), so I'll broaden the search. I hope we can exclude numbers beginning with zero, which could otherwise confound the fourth root interpretation.

 


  Posted by ed bottemiller on 2008-08-04 11:26:27
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information