Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.


bert
Posts:
396
Registered:
1/4/06


Re: 8x8 bit patterns
Posted:
Mar 1, 2013 8:57 AM


On Thursday, February 28, 2013 10:51:02 AM UTC+1, Martin Brown wrote: > I have a little puzzle where I think the answer is that it is not > possible but having tried all the tricks I can think of cannot prove it. > > The problem arises from considering the possible bit patterns in an 8x8 > JPEG encoding square and searching for one that includes all possible > states for subsampling up to 2x2  that is 2x1, 4x1, 2x2 > > It is obvious that the 4x1 subsampling requirement means that the final > solution if it exists must be a permutation of the nibbles 0,1,...,15
No, I think that's quite unlikely to be true, on the basis that there are one or two 16bit strings which, cyclically, contain all sixteen nibbles (I remember using them as read/write patterns in disk tests). One 8bit row of your square can contain five different nibbles, not just two. 



