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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.)
Challenge | Comment 4 of 11 |

I agree with Charlie's approach -- initially I had limited my range to two three-digit numbers-- and found the same ages.

As a challenge: if the mother may be the younger (but retaining the other constraints), find solutions where the sum of the ages of mother and father is (1) a product of two distinct primes (not including 1), and (2) a product of three distinct primes.  In the second case the difference in their ages is a multiple of the age difference in the first case.


  Posted by ed bottemiller on 2008-08-04 17:39:33
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