I thought 0xCCCCCCCD was a very nice number so I asked myself why it would come out like that. I wondered whether

0.CCCCCCCC.... = 4/5 had anything to do with it.

Using hexadecimal we have

    5 * 3 = 10 - 1, so 
    5 * C = 40 - 4 so
    5 * (1 + C + C0 + C00 + C000...) = 5 - 4 + 40 - 40 + 400... where the last term is = 0 mod 2^32
         -----
           D

This relates to

    0.CCCCCC.... = 4 / 5

Because in order for that to come out right, multiplying 0.CCCC... with 5 has to have all intermediate terms cancel, leaving only a 4.

So why would it take its digit from 4 / 5 and not 1 / 5? Because it takes x=4 to make the 5-x subtraction in 5 - x + x0 - x0 + x00 to come out to 1.

So this gives us a general rule for inversion (for numbers less than 16). Take the hexadecimal expansion of (n-1) / n, truncate to get enough hex chars, add 1 to the least significant hex digit.

I.e. the inversion of 3 would be 0xAAAAAAAB