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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

   -281474976710655  


with replacement of the random selection by

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

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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