Roman Number Lengths

  1. What is the smallest valued number which can be written with N Roman Numerals (1<=N<=20)? Remember a bar over a number represents multiplication by 1000; don't count a bar as a numeral. For example:
    _
    X = 10,000, using 1 Roman Numeral.
  2. What are the longest and largest numbers written with Roman Numerals with the restrictions of no bars allowed, and a maximum of one leading M.

Source: Original, but I wouldn't be surprised to find it elsewhere.


Solutions were received from Nick McGrath and Alan O'Donnell. Nick's answers are below:
1)   1 numeral   I=1
    2:   II=2
    3    III=3
    4    VIII=8
    5    XVIII=18
    6    XXVIII=28
    7    XXXVIII=38
    8    LXXXVIII=88
    9    CLXXXVIII=188
    10    CCLXXXVIII=288
    11    CCCLXXXVIII=388
    12    DCCCLXXXVIII=888
    13    MDCCCLXXXVIII=1888
    14    MMDCCCLXXXVIII=2888
    15    MMMDCCCLXXXVIII=3888
          _
    16    VMMMDCCCLXXXVIII=8888
          __
    17    XVMMMDCCCLXXXVIII=18888
          ___
    18    XXVMMMDCCCLXXXVIII=28888
          ____
    19    XXXVMMMDCCCLXXXVIII=38888
          _____
    20    LXXXVMMMDCCCLXXXVIII=88888
 
 
2) Longest   MDCCCLXXXVIII = 1888
 
   Largest    MCMXCIX = 1999

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