If the positive integers up to a million are ordered alphabetically (spelled out in English), at what...

By my count, using English spellings for the numbers, it's preceded by
all of the following (not in this order)

      400,000s, 500,000s, 800,000s, 900,000s  ->  400,000 numbers
      40,000s, 50,000s, 80,000s, 90,000s  ->  40,000 numbers
      4,000s, 5,000s, 8,000s, 9,000s  ->  4,000 numbers
      400s, 500s, 800s, 900s  ->  400 numbers
      40s, 50s, 80s, 90s  ->  40 numbers
      4, 5, 8, 9, 11, 14, 15, 18, 19  ->  9 numbers

for a total of 444,449 numbers.  So "one" is 444,450th.

[ Editor: the list omits 11,000-11,999, 14,000-14,999, 15,000-15,999,
18,000-18,999 and 19,000-19,999 ("eleven thousand ...", "fourteen
thousand ...", etc.), which also precede "one": 5 x 1,000 = 5,000 more
numbers. ]

By the way, this assumes that the correct spellings for 100, 1000, 1e5
and 1e6 are "one hundred", "one thousand", etc., not "hundred" or "a
thousand", etc.  If I'm wrong, my total could change by up to 4.

-- Tom Magliery <mag@ncsa.uiuc.edu>

In article <399qr0$de8@portal.gmu.edu>, John H Ward
<jward1@mason1.gmu.edu> wrote:
>If the positive integers up to a million are ordered alphabetically,
>at what position is one?

Below 20 it would rank   10th, by enumeration: 4, 5, 8, 9, 11, 14, 15,
                         18, 19.
Below 100 we have        40 more: 40-59 and 80-99
From 100-999 we have    400 more: 400-599 and 800-999 [Editor:
                         "800-899" in the original]
From 1000-9999 we have 4000 more.

I make it 444,450.

-- Jim Gillogly <jim@acm.org>