I have chosen 3 different whole numbers less than 10, and have found several simple combinations that lead to perfect squares. Calling the numbers x,y, and z, the following combinations all yield a perfect square as the answer. (A perfect square is a number that has a whole number square root).

(x^2)y + (y^2)z + (z^2)x

x+y+z

z-y-x

xyz

(x^2)(z-1)

There are also several more complicated arrangements that lead to perfect squares, such as

x((z^2)-1)+z((y^2)-3)-x(yz-xy)

2xz+x+z

x((z^2)+x)+z(y^2)-(x^2)(z-y)

Given that these perfect squares are all different, and range between 0 and 100 (inclusive), can you determine x,y, and z?

(In reply to re: Zero? by Fernando)

In Canadian Classrooms anyways (there are discrepancies between systems unfortunately), the set of "Natural" numbers is more commonly known as counting numbers, Whole numbers include the counting numbers and zero (easily remembered by considering the "o" in whole as a zero), and integers are counting numbers, zero and the negatives of the counting numbers. I apologize if this nomenclature is not standard in the US or elsewhere.

Posted by Cory Taylor on 2003-03-31 17:18:41