MathDB

The numbers

\frac 32

\frac 43

and

\frac 65

are intially written on the blackboard. A move consists of erasing one of the numbers from the blackboard, call it

a

, and replacing it with

bc-b-c+2

, where

b,c

are the other two numbers currently written on the blackboard. Is it possible that

\frac{1000}{999}

would eventually appear on the blackboard? What about

\frac{113}{108}

?
(Andrei Bâra)

Problem Statement