Re: Roman numerals (was: Re: Discouraging...)

Johan de Koning (k.i...@12345net.nl) wrote:
: Sure, that rules out MXM.
: But then again, what is 1 unit down, eg
: 450 = LD or CCCCL,
: 490 = XD or LDXXXX or CCCCXC ?

Both wrong. 450 = CDL, 490 = CDXC. Although the Romans themselves
weren't particularly consistent about abbreviating sequences of four
identical characters, so 490 could also be CCCCXC, CDLXXXX or even
CCCCLXXXX.

The easiest way to understand it is to realize that you can separate
any roman numeral into digits: 1998 = M DM LC VIII. Each digit has
the same form as the lowest, (1=I, 2=II, 3=III, 4=IV, 5=V, 6=VI,
7=VII, 8=VIII, 9=IX) only the letters used vary between the groups.
Of course there's no letter for 5000, so the largest number that
can be represented like this is 3999 = MMMDMLCIX. (How's that for a
year4k bug?)

Another way to do it is using a two-pass process, first creating an
expanded number by starting with M, putting as many (0-4) of them
as fit in the number, then moving to the next lower letter. The
second pass consists of replacing each AAAA with AB, where B=5*A,
and then each BAB with AC, where C=10*A.