From: Rob Biedenharn <Rob@...>
Date: 2009-11-12T01:02:25+09:00
Subject: Re: Roman Numerals (Arrgh!)

On Nov 11, 2009, at 10:51 AM, Gennady Bystritsky wrote:
> On Nov 11, 2009, at 5:35 AM, Rob Biedenharn wrote:
>>>> And with an appropriately formed $numerals array, the "subtraction
>>>> rule" is already covered. ;-)
>>>
>>> Would you please elaborate? You mean same algorithm and "better"
>>> $numerals would cover mapping of 4 => "IV", 9 => "IX", etc.?
>>>
>>>>
>>>> -Rob
>>
>> Yes, that's it exactly. Testing/using 9 before 5, you find IX (and
>> stop) before you go to VIIII. You can't repeat one of the  
>> "subtraction
>> groups" the way that you can repeat the individual numerals: 8 is
>> always VIII and never IVIV or IIX
>
> Now you intrigued me ;-). So I am asking directly -- given the  
> following $numerals:
> $numerals = [[1000, "M"], [500, "D"], [100, "C"], [50, "L"], [10,  
> "X"], [5, "V"], [1, "I"]]
>
> ...how one can transform it so that the original algorithm would  
> produced shortened roman numbers? Please present the exact value of  
> $numerals satisfying the above condition.
>
> Gennady.


[[1000, "M"], [900, "CM"], [500, "D"], [400, "CD"], [100, "C"], [90,  
"XC"], [50, "L"], [40, "XL"], [10, "X"], [9, "IX"], [5, "V"], [4,  
"IV"], [1, "I"]]

Q.E.D.  (I think that's Latin for "So there!" ;-)

-Rob

Rob Biedenharn		http://agileconsultingllc.com
Rob@AgileConsultingLLC.com