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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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Some Thoughts solution for 4 elements only | Comment 10 of 11 |
 The following program evaluates a reduced version of the given set: just the first four values. There are 5!! = 1*3*5 = 15 potential results, and in fact, each of these results is indeed different, as UBASIC shows the resulting fractions in reduced form. It also uses double virgules rather than single, to separate denominator from numerator.
 
    4   open "ratvalv2.txt" for output as #2
   30    dim V(4)
   36    for I=1 to 4
   37      V(I)=49//I
   38    next
   39    a=v(1):b=v(2):c=v(3):d=v(4)
   40    print #2,fnF(fnF(fnF(a,b),c),d)
   50    print #2,fnF(fnF(fnF(a,b),d),c)
   60    print #2,fnF(fnF(fnF(a,c),b),d)
   70    print #2,fnF(fnF(fnF(a,c),d),b)
   80    print #2,fnF(fnF(fnF(a,d),b),c)
   90    print #2,fnF(fnF(fnF(a,d),c),b)
  100    print #2,fnF(fnF(fnF(b,c),a),d)
  110    print #2,fnF(fnF(fnF(b,c),d),a)
  120    print #2,fnF(fnF(fnF(b,d),a),c)
  130    print #2,fnF(fnF(fnF(b,d),c),a)
  140    print #2,fnF(fnF(fnF(c,d),a),b)
  150    print #2,fnF(fnF(fnF(c,d),b),a)
  160
  170    print #2, fnF(fnF(a,b),fnF(c,d))
  180    print #2, fnF(fnF(a,c),fnF(b,d))
  190    print #2, fnF(fnF(a,d),fnF(b,c))
  310   close #2
  399   end
  400   fnF(x,y)
  410     local vl
  420     vl=x*y-x-y+1
  430   return(vl)           


 777585//4 
 1166353//6 
 1554435//8 
 1554337//8 
 582613//3 
 1165177//6 
 776115//4 
 193992 
 581486//3 
 193796 
 386857//2 
 193404 
 386561//2 
 1548645//8 
 581042//3 


  Posted by Charlie on 2016-03-22 08:12:50
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