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www/statics/euler/Euler_Problem-089_description.md

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+For a number written in Roman numerals to be considered valid there are basic rules which must be followed.
+Even though the rules allow some numbers to be expressed in more than one way there is always a "best" way
+of writing a particular number.
+
+For example, it would appear that there are at least six ways of writing the number sixteen:
+
+~~~
+IIIIIIIIIIIIIIII
+VIIIIIIIIIII
+VVIIIIII
+XIIIIII
+VVVI
+XVI
+~~~
+
+However, according to the rules only XIIIIII and XVI are valid,
+and the last example is considered to be the most efficient, as it uses the least number of numerals.
+
+The 11K text file, roman.txt, contains one thousand numbers written in valid,
+but not necessarily minimal, Roman numerals;
+see **About... Roman Numerals** for the definitive rules for this problem.
+
+Find the number of characters saved by writing each of these in their minimal form.
+
+*Note:* You can assume that all the Roman numerals in the file contain no more 
+than four consecutive identical units.
+
+About... Roman Numerals
+=======================
+
+> How do you read and write Roman numerals?
+
+Traditional Roman numerals are made up of the following denominations:
+
+~~~
+I = 1
+V = 5
+X = 10
+L = 50
+C = 100
+D = 500
+M = 1000
+~~~
+
+In order for a number written in Roman numerals to be considered valid there are three basic rules 
+which must be followed.
+
+Numerals must be arranged in descending order of size.
+
+`M`, `C`, and `X` cannot be equalled or exceeded by smaller denominations.
+
+`D`, `L`, and `V` can each only appear once.
+
+For example, the number sixteen could be written as `XVI` or `XIIIIII`,
+with the first being the preferred form as it uses the least number of numerals.
+We could not write `IIIIIIIIIIIIIIII` because we are making `X` (ten) from smaller denominations,
+nor could we write VVVI because the second and third rule are being broken.
+
+The "descending size" rule was introduced to allow the use of subtractive combinations.
+For example, four can be written `IV` because it is one before five.
+As the rule requires that the numerals be arranged in order of size it should be clear to
+a reader that the presence of a smaller numeral out of place, so to speak,
+was unambiguously to be subtracted from the following numeral rather than added.
+
+For example, nineteen could be written `XIX` = `X (ten) + IX (nine)`.
+Note also how the rule requires `X` (ten) be placed before `IX` (nine),
+and `IXX` would not be an acceptable configuration (descending size rule).
+Similarly, `XVIV` would be invalid because `V` can only appear once in a number.
+
+Generally the Romans tried to use as few numerals as possible when displaying numbers.
+For this reason, `XIX` would be the preferred form of nineteen over other valid combinations,
+like `XIIIIIIIII` or `XVIIII`.
+
+By mediaeval times it had become standard practice to avoid more than three consecutive
+identical numerals by taking advantage of the more compact subtractive combinations.
+That is, `IV` would be written instead of `IIII`,
+`IX` would be used instead of `IIIIIIIII` or `VIIII`, and so on.
+
+In addition to the three rules given above,
+if subtractive combinations are used then the following four rules must be followed.
+
+ - Only one `I`, `X`, and `C` can be used as the leading numeral in part of a subtractive pair.
+ - `I` can only be placed before `V` and `X`.
+ - `X` can only be placed before `L` and `C`.
+ - `C` can only be placed before `D` and `M`.
+
+Which means that `IL` would be considered to be an invalid way of writing forty-nine,
+and whereas `XXXXIIIIIIIII`, `XXXXVIIII`, `XXXXIX`, `XLIIIIIIIII`, `XLVIIII`, and `XLIX`
+are all quite legitimate, the latter is the preferred (minimal) form.
+However, minimal form was not a rule and there still remain in Rome many examples
+where economy of numerals has not been employed.
+For example, in the famous Colosseum the numerals above the forty-ninth entrance
+is written `XXXXVIIII` rather than `XLIX`.
+
+It is also expected, but not required, that higher denominations should be used whenever possible;
+for example, `V` should be used in place of `IIIII`, `L` should be used in place of `XXXXX`,
+and `D` should be used in place of `CCCCC`.
+However, in the church of Sant'Agnese fuori le Mura (St Agnes' outside the walls),
+found in Rome, the date, `MCCCCCCVI` (1606), is written on the gilded and coffered wooden ceiling;
+I am sure that many would argue that it should have been written `MDCVI`.
+
+So if we believe the adage, "when in Rome do as the Romans do,"
+and we see how the Romans write numerals, then it clearly gives us much more freedom
+than many would care to admit.