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?

We all seem agreed on the answer to the original problem, but I suspect we all used computer assistance, thru a program, a spreadsheet or similar, and I suppose we all used at least a calculator to get the fourth powers/roots aspect.  The original setter of the problem asked if a solution could be derived without such assists (where's Windy??).  Did anyone try to create equations to solve the problem, and use those alone?

If any one is not now bored with the problem, I suggest a related challenge (in my previous post).

Posted by ed bottemiller on 2008-08-05 10:42:50