What do the numbers in square brackets mean beside the TAoCP exercises?

Question

Here is an example:

1. [00] The binary form of 2009...
2. [05] Which of the letters...
3. [10] Four-bit quantities -- half-bytes, or hexadecimal digits...
4. [15] A kilobyte...
5. [M13] If x is any string of 0s and 1s...
6. [M20] Prove or disprove...

What do the [00], [05], [10], [15], [M13], [M20] mean?

I have tried:

• Googling taocp exercises square brackets
• looking for a pattern in the square-bracketed numbers.
  • they both increase and decrease
  • they are mostly but not all multiples of five
  • the ones with an M appear every now and then
  • M is the only prefix
  • the codes are non-unique
• Googling "the art of computer programming" exercises brackets
• Googling "the art of computer programming" M13
  • Viewing http://dl.acm.org/citation.cfm?id=1312683, which indicates M means milestone.
• Googling "the art of computer programming" [00]
• Looking for an appendix in the book that explains
• Considering the > that is beside some questions too

No luck!

Answer 1

I think this is mentioned in the introduction to the book somewhere (my copy is in my office now). If I remember correctly, the numbers indicate difficulty, with numbers beginning with 0 being warm-up questions, numbers beginning with 3 indicating problem-set level questions, numbers beginning with 4 indicating very hard problems, and 50 meaning extremely hard (possibly open) questions.

The M means "math," as in "you'll need some tricky math here." The HM means "higher math," meaning "you'll need math beyond what we've covered here to solve this problem."

Hope this helps!

Answer 2

On page xvii in the text there is a summary of the notation used with the exercises

► = recommended
M = Mathematically oriented 
HM = Requiring "higher math"
00 = Immediate
10 = Simple (one minute)
20 = Medium (quarter hour)
30 = Moderately Hard
40 = Term Project
50 = Research Problem

It's meant to be a roughly logarithmic scale. Furthermore "The remainder of the rating number divided by five indicates the amount of detailed work required. Thus , an exercise rated 24 may take longer to solve than an exercise that is rated 25, but the latter will require more creativity" -P. XVI (notes on the exercises)