Roman Numerals

The biggest numeral smaller than 400 is the C for 100. But I can't do CCCC for the 400, because that's four of the same character in a row. Instead, I have to subtract 100 from 500: CD = 500 − 100 = 400.

The 50 is easy: that's just L. For the 3, I use three Is. Then my answer is:

The largest number-character less than 1900 is 1000: M. After taking care of the thousand, I've got the 900 part of the number. I could start with a D for 500 and then add four Cs for the 400, but I can't use four of the same character in a row. So I'll instead use subtraction to get the 900: one hundred from one thousand is nine hundred, so 900 = CM.

The next part of the number is the 80; the largest number-character smaller than this is L for 50. Then I'll add three Xs for the three tens: 80 = LXXX. I'm left then with the nine, which is written as "one from ten": IX. Putting it all together, I get:

At the start of this Roman number is M which is 1000. Then comes D which is 500, followed by three Cs which is 300, for a total of 800. Then I've got an X which is 10, but that's followed by another C, which means that the 10 is subracted from the 100. In other words, the XC is a 100 − 10 = 90. After that comes VII which I recognize as being 5 + 1 + 1 = 7.

The first digit here is M, which stands for 1000. The next digit is a C, which stands for 100, but it's followed by an M, so this tells me that the C is actually subtracted from this second M. This means that the CM stands for 1000 − 100 = 900. Next come three X's, which is three tens, for 30. Then there's an I, but it's immediately followed by another X, which means that the I is subtracted from the X, giving me 10 − 1 = 9.

Putting it all together, I get:

You might think that I could just subtract one from five hundred: ID. But that's too much of a subtraction.

In general, I can only subtract 1, 10, or 100 from the next one or two numerals bigger. That is, I can subtract 1 from 10 or 50, but not from anything bigger; I can subtract 10 from 50 or 100; and I can subtract 100 from 500 or 1,000, but that's it. (Why? "Because".) So I have to add up to 499, rather than subtracting down from 500.

The biggest numeral smaller than 499 is 100, but I can't add up to 100 by using four Cs; instead, I have to subtract 100 from 500 to get 400. This leaves me with the 99. While I can't subtract a 1 from a 100 to get 99, I can subtract a 10 from 100 to get 90. Then I can subtract a 1 from a 10 to get 9. Putting it all together, I get: