The infinite pairs of numbers whose sum equals their product is described by:

x + y = xy

x = xy - y

x = y(x-1)

x/(x-1) = 1 + 1/(x-1) = y

In the above example x = AB and y = C.DE.

This is a big clue. It tells me the number y always begins with "1". So now I know C = 1.

I know that 1/(x-1) = 1/(AB-1) = ??/100. This means that x-1 divides 100. This means that AB can only be 51, 26, or 21.

Since C = 1 and A & B cannot be 1, this leaves only 26.

This means that:

A=2

B=6

C=1

D=0

E=4
 

To return to original question, Click Here.