[superprismatic]

If we were to write the numbers from 1 to 2001 in Roman numeral notation

(see http://www.novaroma.org/via_romana/numbers.html ) and sort this list

alphabetically, what would be the number in the middle (1001^st in the list)?

You can use the converter on the web site to check the way you form numbers

using Roman numerals.

[Guest]

The sequence starts with the numbers from 100 to 499 and from 900 to 999 (500 total), then the ones from 500 to 899 (400), then 1,2,3,4 and 9, then the numbers from 50 to 89 (40) then 36 more for 1000,1001..., 1100, 1101... and so on, then 1350,1351... until the 1001st number, which I think is 1368. I kinda lost my patience with this and I don't even know if I did it right, so here it goes.

Edited June 8, 2010 by archlordbr

[Guest]

if archlordbr is correct then

1368 in roman numerals is

MCCCLXVIII

[Guest]

1391

[Guest]

1391 is MCCCXCI

[Guest]

MCCCXCI

[Guest]

Brute force method!

MCCCXCI 1391

Using a bash shell created the following script to convert decimal to roman numeral (Do multiple parenthesis work in roman numerals beyond 5 million?):

$>cat roman_numeral.sh 

#!/bin/bash


number=$1

roman=""


iteration=0;

ones_base=( "I" "X" "C" )

fives_base=( "V" "L" "D" )

ones=( $ones_base )

fives=( $fives_base )


if [[ ! $number =~ '^[0-9]+$' ]] ; then

        echo "Only argument is a single decimal number"

fi


while [[ $number -gt 0 ]] ; do

        nextitr=$(( $iteration + 1 ))

        openp=$( for (( re=0; re < $(( $nextitr / 3 )); re++)) ; do echo -n '('; done )

        closep=$( for (( re=0; re < $(( $nextitr / 3 )); re++)) ; do echo -n ')'; done )

        fives[$nextitr]="${openp}${fives_base[$nextitr % 3]}${closep}"

        openp=$( for (( re=0; re < $(( ($nextitr - 1) / 3 )); re++)) ; do echo -n '('; done )

        closep=$( for (( re=0; re < $(( ($nextitr - 1) / 3 )); re++)) ; do echo -n ')'; done )

        ones[$nextitr]="${openp}${ones_base[$nextitr % 3]}${closep}"

        remainder=$(( $number % 10 ))

        case $remainder in

         1)

                roman="${ones[$iteration]}${roman}" ;;

         2)

                roman="${ones[$iteration]}${ones[$iteration]}${roman}" ;;

         3)

                roman="${ones[$iteration]}${ones[$iteration]}${ones[$iteration]}${roman}" ;;

         4)

                roman="${ones[$iteration]}${fives[$iteration]}${roman}" ;;

         5)

                roman="${fives[$iteration]}${roman}" ;;

         6)

                roman="${fives[$iteration]}${ones[$iteration]}${roman}" ;;

         7)

                roman="${fives[$iteration]}${ones[$iteration]}${ones[$iteration]}${roman}" ;;

         8)

                roman="${fives[$iteration]}${ones[$iteration]}${ones[$iteration]}${ones[$iteration]}${roman}" ;;

         9)

                roman="${ones[$iteration]}${ones[$nextitr]}${roman}" ;;

        esac

        (( number /= 10 ))

        (( iteration++ ))

        if [[ $iteration -eq 2 ]] ; then

                ones_base[0]="M"

        fi

done


echo $roman

The sorting:

$>for (( re=1; re <= 2001; re++ )) ; do echo "`./roman_numeral.sh $re` $re"; done | sort | awk 'NR == 1001'

MCCCXCI 1391

What method did everyone else use?