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Roman Resolve (Posted on 2013-05-08) Difficulty: 3 of 5
All the roman numerals are written down in ascending order, without commas or spaces, as follows:
IIIIIIIVVVIVIIVIIIIXXXIXII…….
What are the respective 2013th letter and the 10000th letter in the above sequence?

Note: Each of M, D, C and L also qualifies as a roman numeral. For example, the number 1782 would be denoted MDCCLXXXII in Roman numerals.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution | Comment 1 of 2

n = 1: lenct = 1
DO
  n = n + 1
  q = n \ 1000: r = n MOD 1000
  r$ = STRING$(q, "M")
  n2 = r
  q = n2 \ 100: r = n2 MOD 100
  SELECT CASE q
     CASE 9: r$ = r$ + "CM"
     CASE 5 TO 8: r$ = r$ + "D" + STRING$(q - 5, "C")
     CASE 4: r$ = r$ + "CD"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "C")
  END SELECT
  n2 = r
  q = n2 \ 10: r = n2 MOD 10
  SELECT CASE q
     CASE 9: r$ = r$ + "XC"
     CASE 5 TO 8: r$ = r$ + "L" + STRING$(q - 5, "X")
     CASE 4: r$ = r$ + "XL"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "X")
  END SELECT
  n2 = r
  q = n2
  SELECT CASE q
     CASE 9: r$ = r$ + "IX"
     CASE 5 TO 8: r$ = r$ + "V" + STRING$(q - 5, "I")
     CASE 4: r$ = r$ + "IV"
     CASE 0 TO 3: r$ = r$ + STRING$(q, "I")
  END SELECT
  newlen = lenct + LEN(r$)
  IF lenct < 10 AND newlen >= 10 THEN
    PRINT n, r$, 10 - lenct, MID$(r$, 10 - lenct, 1), "10"
  END IF
  IF lenct < 2013 AND newlen >= 2013 THEN
    PRINT n, r$, 2013 - lenct, MID$(r$, 2013 - lenct, 1), "2013"
  END IF
  IF lenct < 10000 AND newlen >= 10000 THEN
    PRINT n, r$, 10000 - lenct, MID$(r$, 10000 - lenct, 1), "10,000"
    END
  END IF
  lenct = lenct + LEN(r$)
LOOP

(with much of the code borrowed from the solution to Roman Trivia)

finds

6            VI             1            V             10
376          CCCLXXVI       8            I             2013
1618         MDCXVIII       4            X             10,000

with the first line being just a sanity check, that the 10th position in the string is the V that's the 1st letter of VI, the roman numeral for 6.

The 2013th letter is I, the 8th character of CCCLXXVI, the roman numeral for 376.

The 10,000th letter is X, the 4th character of MDCXVIII, the roman numeral for 1618.


  Posted by Charlie on 2013-05-08 12:50:21
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