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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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Hints/Tips Two special results | Comment 2 of 11 |
(In reply to a sampling of 500 at random by Charlie)

  If the process starts at the left and continues to the right at each step of the way, the results are
   81286165137705819192432328 / 244977040951739008680100275  ~=  0.3318113600438147358 
  If the process starts at the right and continues to the left at each step of the way, the results are the integer


with replacement of the random selection by

for r=97 to 1 step -1
   if used(r) = 0 then cancel for: goto 90

and variation for the forward direction (1 to 97) and use of line number 130 for the second selected number.

Edited on March 20, 2016, 10:31 am
  Posted by Charlie on 2016-03-20 10:26:59

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