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Roman Trivia (Posted on 2009-05-17) Difficulty: 2 of 5
Take all the Roman numbers (using the modern standard subtractive notation in which IV = 4, IX = 9, XL = 40, XLIX = 49, XC = 90, etc.) from I to M (1 to 1000)...

1. Which number has the most Roman letters?

2. If you group them by the number of Roman letters, which group has the most members?

3. How many numbers start with C?

4. There is something interesting about the groupings in #2. What is it?

See The Solution Submitted by Sing4TheDay    
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Solution computer solution | Comment 2 of 5 |
1. The longest has 12 letters:  DCCCLXXXVIII = 888

2. The group with the most members is length 6:


1   2   3    4    5    6    7    8   9  10 11 12
7  24  62  123  180  208  180  123  62  24  6  1

3. There are 500 beginning with C: the 100's, 200's, 300's, 400's and 900's.

 

4. The pattern is symmetrical except for the 7 that have length 1 vs the 6 of length 11 and 1 of length 12.

 

CLS
DIM lCt(20)
FOR n = 1 TO 1000
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$(q, "I")
END SELECT
  IF LEN(r$) > longestSize THEN
   longestSize = LEN(r$): longest$ = r$: longestn = n
  END IF
  lCt(LEN(r$)) = lCt(LEN(r$)) + 1
  IF LEFT$(r$, 1) = "C" THEN cCt = cCt + 1
NEXT
PRINT

PRINT longestSize, longest$, longestn
FOR i = 1 TO 12
   PRINT lCt(i);
NEXT
PRINT
PRINT cCt

 

 

 


  Posted by Charlie on 2009-05-17 15:53:13
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