The challenge states that the image includes shades of gray, #000000 to #F5F5F5. Since all of the pixels are gray, all three bytes of each color will be identical, so only one needs to be considered.
#000000-#F5F5F5 leaves shades 0-245 possible, significantly more than the 50 shades the challenge includes. Dividing these possible shades up evenly, it can be reasonably assumed that each shade is 5 apart.
Next, I wrote a simple Javascript program which would find each possible shade in the image. The shade that is not found is clearly the missing one.