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A cancellation fallacy (Posted on 2013-01-18) Difficulty: 3 of 5
Sometimes an arithmetic procedural error produces a correct answer.
An accidental cancellation is reducing a fraction by canceling individual digits in the numerator and denominator.

In some cases the result is equal to that obtained by a correct process.
Examples:
16/64 = 16/64 = 1/4;
26/65 = 26/65 = 2/5;
266/665 = 266/665 = 2/5;
49/98 = 4/8 = 1/2 etc.

Try to find two-digit cases in bases other than base 10,(e.g. 13/32 = 1/2 ( the only solution in base 4).

No Solution Yet Submitted by Ady TZIDON    
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Hints/Tips re: computer solutions -a partial errata | Comment 2 of 3 |
(In reply to computer solutions by Charlie)

CH,

Please debug your program,- many irrelevant results.

e.g. in base 10

     13/65=1/5   10         ok 
     15/75=1/5   10    not 1/7
    16/32=1/2   10    nothing to cancel
    16/64=1/4   10    ok
    16/96=1/6   10    not 1/9
    17/85=1/5   10     nothing to cancel 
    19/95=1/5   10    ok
    26/65=2/5   10    ok 
    27/54=2/4   10    nothing to cancel
    38/76=3/6   10   nothing to cancel
    39/65=3/5   10  nothing to cancel
   49/98=4/8   10   ok

Another example :.... different triviality, that can't come up in base 4 is exemplified by the decimal 21/42, where ....

Should be 1/2 not 1/4

Your output apparently lists cancellations that not necessarily produce the right answers...

   Please check other bases as well.


  Posted by Ady TZIDON on 2013-01-18 19:38:23
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