# Description

From Horia:
possible improvements in the understanding of this activity (i.e., the help section, which seemed to me pretty hard to understand, even for an average adult).

The roman numbers are all built out of these 7 numbers: I and V (units, 1 and 5), X and L (tens, one and five), C and D (hundreds, one and five), and M (thousand). An interesting observation here is that the roman system of numbers lacks the number 0!

All the units except 4 and 9 are built using sums of I and V: I, II, III, V, VI, VII, VIII.

The 4 and the 9 units are built using differences: IV (5 – 1) and IX (10 – 1).

All the tens except 40 and 90 are built using sums of X and L: X, XX, XXX, L, LX, LXX, LXXX.

The 40 and the 90 tens are built using differences: XL (10 taken from 50) and XC (10 taken from 100).

All the hundreds except 400 and 900 are built using sums of C and D: C, CC, CCC, D, DC, DCC, DCCC.

The 400 and the 900 hundreds are built using differences: CD (100 taken from 500) and CM (100 taken from 1000).

Sums of M are used for building thousands: M, MM, MMM.

Notice that you cannot join more than three identical symbols. The first implication of this rule is that you cannot use just sums for building all possible units, tens or hundreds, you must use differences too. On the other hand, it limits the maximum roman number to 3999 (MMMCMXCIX).

The building of the roman numbers is made up by an agglutination of numbers (the thousands, joined with the hundreds, joined with the tens, joined with the units → just like the arab decimal system). This agglutination of numbers is interpreted as the sum of these particular numbers (again → just like the arab decimal system: you add up thousands+hundreds+tens+units, and you write the respective figures combined).

Examples:

2394: we got a sum of 2000 (MM), 300 (CCC), ninety (XC) and 4 units (IV), so we write this sum conjoined: MMCCCXCIV

MMMCMXLIX: we got first thousands (MMM=3000), then we got hundreds (CM=1000–100=900), then we got tens (XL=50–10=40), and at last we got units (IX=10–1=9), so we write them combined, in the decimal system: 3949).