Tuesday, June 8, 2010

Roman Numerals, and a Classic Error

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Roman-NumeralsWhen a number appears in a cryptic clue, a possible interpretation is that its Roman numeral has to be substituted to get the answer.

Examples:

Times 24440: Insects: bumping fifty off takes such an age (3) ICE
                     LICE (insects) – L (Roman numeral for 50)

FT 13332 (Sleuth): Surpass 40 in Rome, we hear? (5) EXCEL
                            Homophone of XL (Roman numeral for 40)

The number may be well-disguised, as in:

Times 23960: Businessman returning about half of score composed (7) RELAXED
                     DEALER (businessman) reversed, around X (Roman numeral for 10, which is half of score i.e. 20)

Roman Numerals: Quick Reference Table

Setters have more use for a number like 100 (Roman numeral: C) than 123 (Roman numeral: CXXIII).

A quick reference table for the numbers you are most likely to encounter in clues:

Number Roman Numeral
1 I
2 II
3 III
4 IV
5 V
6 VI
7 VII
8 VIII
9 IX
10 X
11 XI
40 XL
50 L
Number Roman Numeral
51 LI
55 LV
60 LX
90 XC
100 C
101 CI
200 CC
400 CD
500 D
600 DC
1000 M
1001 MI
2000 MM

Spot The Error

We may come across published clues like the next three, but there is something wrong with them. Do you see the error?

NIE 13-Aug-09: Fifty is under forty-nine? Well, no (3) ILL

THC 9454 (Sankalak): One making an earnest appeal to displace about 99 (10) SUPPLICANT

Guardian 24643 (Gordius): It melts for about 99 bucks (2-4) DE-ICER

Update (08-Jun-2010): Congrats to GreenMangoMore, Anon, maddy, gnomethang, Balaji, veer, Sanjeev (on twitter), raju for getting it right. For those still in the dark, the explanation:

The Classic Roman Numeral Mistake

On the face of it, IL and IC appear to follow the same subtractive principle as IV and IX, i.e. IL = L (50) - I (1) = 49.

This is actually not valid.

The subtractive principle for Roman numbers has these restrictions:
You can only subtract a power of ten, and only from the next two higher "digits", where the digits are {I, V, X, L, C, D, M}.

That is, only I, X and C can be subtracted, AND
I can be subtracted only from V and X; X can be subtracted only from L and C; C can be subtracted only from D and M.

By these rules, the Roman numerals IL for 49 and IC for 99 do not work.
The correct representation for 49 is XLIX, for 99 is XCIX.

Veer mentions "cryptic licence". Given that we see so much of IC and IL even in the careful setters' clues, that is perhaps the sensible-liberal way to look at it - but to me it still seems wrong!

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18 comments

GreenMango More said...

He he..49 is actually XLIX and 99 is XCIX.

Great catch Shuchi! So you're so good at this that you know the mistake setters make and crack it anyway :)

Anonymous said...

1) 49 is not IL(100-1) rather XLIX(40+9)
2), 3) 99 is not IC rather XCIX(90+9)

maddy said...

Shuchi,
Nice post.

Rules for roman numerals say that the smaller number to be deleted should be 1/5 or 1/10 the larger number , Hence, IL for forty nine is not correct, since 1 = 1/50 of 50.
Forty nine = XLIX 'not'IL

Also a number cannot be subtracted from another that is more than ten times greater than it, ie 'I'(one) can't be subtracted from 'C'(hundred) to get IC or ninety nine
Ninety nine = XCIX 'not' IC

gnomethang said...

There was a similar IC problem in DT26259 at the weekend!

Balaji said...

Is it that 49 = XLIX not IL and similarly, 99 = XCIX and not IC.

veer said...

49 = XLIX
99 = XCIX

But, maybe, a cryptic license is allowed for IL and IC along the lines of poetic license...?

raju umamaheswar said...

Supplant is ok, but 99 should be xcix and NOT ic in roman letters.Incorrect ?

Raju Umamaheswar

veer said...

I do agree that it is wrong as the rules do not permit in the Roman number system.

It is curious though, that, both IL and IC are listed as an adjective meaning nine more than forty and nine more than ninety in atleast one source: http://dictionary.babylon.com/il/

Of course, online, I did not find it in the Oxford, Collins, Cambridge or Chambers web dictionaries - do not know if the full edition of any of these have it. I doubt it, as the examples given in the post are not from any Times puzzles..

L N Srinivasakrishnan said...

Very informative post. As usual you have taken a topic of 'crossword' interest and marked it up with research to produce a very readable article of general interest.

Reading your posts is a pleasure.

Shuchi said...

Hi veer

I can imagine my Math teacher from school asking us to rip the horrid page out from that dictionary, in Dead Poets Society style :)

Maybe IC/IL are gaining acceptability through usage? I don't know, but I don't set much store by many online dictionaries. Just run a search and see how many list "fuschia" as a valid word.

An interesting trivia/tip about the Times crossword: They follow a tradition that a number written in numerals always refers to another clue number in the puzzle and not to its Roman representation. Notice that in the Times examples above, L and X come from words "fifty" and "score", not from 50 and 20.

Shuchi said...

@L N Srinivasakrishnan: Thank you!

plutoman said...

At the end of BBC programmes they show the year of production in Roman numerals. So that explains why in 1999 it was MCMXCIX or something like that, not the more logical (to me) MIM.
Thanks!

veer said...

Hi Shuchi: Testing your hypothesis on numbers inside Times clues: If you had solved today's HT puzzle (Times 22634) one down clue was:
8 9 to melt (4)

The same clue in the Times Crossword club was given as:
8 Nine to melt (4)

The crossings indicate T?A?

What does the 9 or nine in the clue refer to? If a clue in the same puzzle, the reference is:
9 Article with favourable slant about a player (8) {THE}{SPI(A)N}

If not, I do not understand how it leads to the logical solution (there is a Thespian called John Thaw in Brit sitcoms). Looking for enlightenment..Thank you

Shuchi said...

Hi Veer

This is clearly a reference to clue no. 9. A double definition, the thespian is John Thaw, who played Inspector Morse in the popular British TV series based on Colin Dexter's novels.

Incidentally, Inspector Morse is an ace Times crossword solver and his sidekick Sergeant Lewis can't make head or tail of cryptic clues. There are some Times-style clues in the Morse books too. (I happen to have read and watched a lot of the Morse series!)

anax said...

The rule in The Times is that a digit in a clue always refers to the appropriate grid entry. All other number references must be spelt out. This rule is simply to avoid confusion.

Shuchi said...

Hi Anax

Thank you for validating that.

veer said...

Anax and Shuchi: Thanks for the clarification. I guess the online version in the Times crossword club just erred and did not take into account the convention in the print version and chose to spell it out.

Shuchi said...

Veer: Both versions look all right. As I understand, the rule is only that a numeral must refer to another grid entry, not that a spelt out word cannot refer to another grid entry.

That is, a grid entry can be referenced using either 9 or 'nine', but IX can only be 'nine', not 9.