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Roman Numerals

Because Roman numerals are based upon simple letter combinations, they are often used in crossword clues.

Roman numerals are constructed out of the basic letter symbols I, V, X, L, C, D and M.  This particularly endears them to crossword compilers, because it allows obscure, but solvable clues to be set for words containing some of the most awkward letters in the English language!

As an aid, the tool below can be used to convert between modern and Roman numerals:

If you are not certain of how Roman numerals are constructed, here is a short guide.

The basic symbols of Roman numerals represent the following values:

 I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000

Other values are made up of repeated sequences of these symbols, combined by some fairly simple rules that follow a fixed pattern.

Two is written as II, and three is III.

Using the same pattern, twenty is XX, thirty is XXX.

Similarly two hundred is CC, three hundred is CCC.

But at four/forty/four hundred, the pattern changes.  Four is represented as 'one less than five',  written as IV; similarly forty is 'ten less than fifty' - XL and four hundred is 'one hundred less than five hundred' - CD.

Five, fifty and five hundred are easy - from the table above..

Then six is one greater than five, written as VI, seven is VII, eight is VIII.  Similarly sixty is LX, seventy is LXX, eighty is LXXX.  Six hundred is DC, seven hundred is DCC, eight hundred is DCCC.

Nine is 'one less than ten', written as  IX, ninety is 'ten less than a hundred' - XC, and nine hundred is 'a hundred less than a thousand' - CM.

There are a few additional rules...

1. Where there are several tens, hundreds, or thousands, any 'less than' modifiers come before the LAST one of the sequence - for example nineteen is always written as XIX, never as IXX.
2. I can only be used as a 'less than' modifier for V and X, not any higher numbers - so ninety-nine cannot be represented as IC, but must be given as XCIX.  It can however be used as a 'more than' modifier for any value, so one hundred and one is CI.
3. Similarly, X can be used as a 'less than' modifier for L and C but not D or M.
4. V, L, and D cannot be used as 'less than' modifiers for anything - forty five cannot be written as VL, it must be given in full as XXXXV.

Given these basic patterns, you can make any number by adding together the representations from the above rules...

• Seventeen = ten + seven = X + VII = XVII
• Forty seven = forty + seven = XL + VII = XLVII
• 1888 (incidentally, the largest Roman number less than 2000) is one thousand + eight hundred + eighty + eight = MDCCCLXXXVIII   (*)
• 1948 (a good year for film makers) is one thousand + nine hundred + forty + eight = M + CM + XL + VIII = MCMXLVIII
• 1988 is one thousand + nine hundred + eighty + eight = M + CM + LXXX + VIII = MCMLXXXVIII
• 1999 = one thousand + nine hundred + ninety + seven = M + CM + XC + IX = MCMXCIX.

Here is a table that can help to build most of the values you are likely to encounter:

 `One` `I` `Two` `II` `Three` `III` `Four` `IV` `Five` `V` `Six` `VI` `Seven` `VII` `Eight` `VIII` `Nine` `IX` `Ten` `X` `Eleven` `XI` `Twelve` `XII` `Thirteen` `XIII` `Fourteen` `XIV` `Fifteen` `XV` `Sixteen` `XVI` `Seventeen` `XVII` `Eighteen` `XVIII` `Nineteen` `XIX` `Twenty` `XX` `Twenty-one` `XXI` `Twenty-two` `XXII` `Twenty-three` `XXIII` `Twenty-Four` `XXIV` `Twenty-Five` `XXV` `Twenty-Six` `XXVI` `Twenty-Seven` `XXVII` `Twenty-Eight` `XXVIII` `Twenty-Nine` `XXIX` `Thirty` `XXX` `Forty` `XL` `Fifty` `L` `Sixty` `LX` `Seventy` `LXX` `Eighty` `LXXX` `Ninety` `XC` `One hundred` `C` `Two hundred` `CC` `Three hundred` `CCC` `Four hundred` `CD` `Five hundred` `D` `Six hundred` `DC` `Seven hundred` `DCC` `Eight hundred` `DCCC` `Nine hundred` `CM` `One thousand` `M` `Two thousand` `MM` `Three thousand` `MMM`

Much of the apparent complexity or Roman numerals arises from the fact that the in common with almost all other numbering systems of the time, the Romans had no symbol for zero, and so a strictly positional-based numerical system was impossible.  This is incidentally why there is no year zero in the calendar - it goes directly from 1 BC to 1 AD, and incidentally explains why it is that we celebrated the millennium a year too soon!

Some sources suggest too that originally, four would have been written as IIII, not IV,  nine as VIIII not IX,  and that the forms that we generally see today were created my medieval monks in order to reduce copying times.  The medieval monks had one major advantage over the Romans - they only had to copy the numbers, not to do arithmetic with them!

However, it is obvious that Roman numbers (however they were written) were relatively clumsy to use for any operations beyond simple addition and subtraction.  This is probably why the Islamic nations, who invented the zero (and the positional number system that included it), were the true mathematicians of the ancient world...

(*) Thanks to Lee Emmert for correcting our mistake on this one.

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