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Rational Value Validation (Posted on 2016-03-20) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
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re(2): cardinality of solution set | Comment 8 of 11 |
(In reply to re: cardinality of solution set by Charlie)

That sequence cannot be the answer to this problem.  1 is in the set and if either X or Y is 1 then Z will be 0.  So the number for this problem is strictly less than the corresponding term in A001147.

Also I noted that to generalize this problem would ask for the 2k-1 rational numbers {k/1, k/2, k/3, ..., k/(2k-1)}.  For k=1 this is just {1}, for k=2 this is {2, 1, 1/3}.  For k=3 this is {3, 3/2, 1, 3/4, 3/5}.

If we could get specific counts for k=1,2,3,4 then we may be able to calculate the answer inductively, or the OEIS might have it.

  Posted by Brian Smith on 2016-03-21 11:38:39
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