The 97 rational numbers 49/1, 49/2, 49/3, ..., 49/97 are written on a blackboard.
Two of the above numbers X and Y are chosen and replaced by X*Y-X-Y+1.
The procedure is repeated until a single number Z(say) remains on the board.

Determine the possible values of Z.

(In reply to cardinality of solution set by Charlie)

I suspect something is wrong with the text of the problem.
Maybe the numbers are reciprocals of what they should be.
The formula X*Y-X-Y+1 also tends to increase the denominator with every step, so maybe this was an error.

I find it hard to believe we are actually to find a set of over a google solutions.

Posted by Jer on 2016-03-21 09:54:59