Is This Number Well Written? Trivia Quiz

Answer:

The Roman numeral system has many peculiarities when it comes to writing it correctly. Let's make a quick recap.

First of all, the Roman Numerals consist of a series of letters, each with a particular value: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000. There is no letter representing zero, and also there is not a way to write negative numbers. These are the most important limitations that the system has in comparison to others.

As a very personal rule of thumb, I will classify symbols as "one-based" and "five-based". In "one-based" I include all symbols that represent a number containing a "1" numeral, and "five-based" includes those that contain a "5" numeral. So, "one-based" includes I, X, C and M, while "five-based" includes V, L, and D. The naming is mathematically inaccurate, and I actually didn't see this classification anywhere, but it comes in handy (at least for me) when expressing certain rules of writing, which we will cover right now.

To write the numbers, the symbols are combined following a series of rules.

Basically:
1 - In general, symbols are arranged from left to right in decreasing order of value. To write 1,500, you should write MD (1000 + 500). The only exception is when we come across a subtractive numeral, which will be discussed shortly.

2 - Symbols can be grouped together, up to three times consecutively, in which case the number represented by them is their sum. This is only valid for "one-based" symbols -- "five-based" are never repeated.
For instance: III -> 1 repeated three times = 3; CC -> 100 repeated two times = 200. You can't write "XXXX" or "MMMM", for instance. You can't write "LL", "VVV" or "DD" either.

3 - If a symbol of lower value appears to the left of a symbol of higher value, you subtract the lower value from the higher value, acting as a subtractive numeral. There are a few sub-rules here:
* Only "one-based" symbols, except for M, can act as a subtractive numeral. You can't write "VX", for example.
* They can only subtract from the two immediately higher symbols: "IV" and "IX" are correct, while "IM", "ID", "IC" and "IL" are not; "XL" and "XC" are ok, "XD" is not.
* The subtractive numeral is only written once, never in groups. "XL" is correct, "XXL" is not.

4 - If a symbol of lower value appears to the right of a symbol of higher value, you add the lower value to the higher value. In this case, any symbol can act as an additive numeral, with the only restriction being the observance of rule #2 ("one-based" symbols can be repeated up to 3 times, "five-based" can't be repeated)

By combining these rules, to read a Roman numeral correctly, go from left to right and form clusters if needed, to help you decide whether to add or subtract based on the relative values of the numerals. Let's focus on the wrong answers and see what's wrong with each of them.

CVXII: "V" can't go before "X"
LIIIV: When used as a subtractive numeral, "I" can't be repeated.
MCCCC: No symbol can be repeated more than 3 times.
XLLV: "L" can't be repeated.
DDCLV: "D" can't be repeated.
MDCCLXVVI: "V" can't be repeated.