Romance in Numbers

Copyright MCMXCVII by Paul Niquette.  All rights reserved.

Length of Roman NumbersAmazing, is it not, that Roman numerals have so many uses in the sciences despite a functional obsolescence in the face of the 'positional notation' afforded by Arabic numerals (see Prolix). There prevails in Roman numerals an undeniable cumbersomeness, and yet these ancient cyphers continue century after century to be printed on pages and chiseled on stones.

The sophisticated solver of this puzzle will recall that there are seven Roman symbols -- I, V, X, L, C, D, M, standing, respectively, for 1, 5, 10, 50, 100, 500, 1,000 in the Arabic numeral system. As fifth-graders used to be taught, you cannot simply read a string of Roman numerals from left to right and translate them into Arabic. There are rules to learn: Only certain combinations are permitted. Not all 49 possible pairs of Roman numerals get applied: VV, LL, DD, for example, give way to X, C, M.

The expression 'greater value' in the subtraction rule is also limited -- you will not find VL or IL for 45 and 49, VC or IC for 95 and 99, VD or ID for 495 and 499, VM or IM for 995 and 999.

The bars in the chart on the right represent the length in number of symbols required to represent the corresponding Arabic number in Roman numerals. In the range of one to a hundred, all but one of those numbers can be expressed in Arabic with only two symbols. Observations...
Almost forgot:
What year in history required the largest number of Roman numerals to express?
MDCCCLXXXVIII
Epilog:  For a puzzle that creates a new classification of numbers, see Reaman Numeral.

Home Page
Puzzle Page
Logic and Reasonings
The Puzzle as a Literary Genre