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 Rational Value Validation (Posted on 2016-03-20)
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 No Rating

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 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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