What is the smallest cardinal number that its standard constructed English name encompasses the most distinct letters of the English alphabet?

My answer: 1,000,001,001,002,568
One-quadrillion, one-billion, one-million, two-thousand, five-hundred sixty-eight.  (With 21 letters of the alphabet)

Lowest number for each letter:
a = thousand     c = none
b = billion         j = none
d = hundred       k = none
e = one             p = none
f = four             z = none
g = eight
h = three
i = five
l = eleven
m = million
n = one
o = one
q = quadrillion
r = three
s = six
t = two
u = four
v = five
w = two
x = six
y = twenty

So we will need 21 letters of the alphabet.

The highest number that has to be included is "quadrillion", with a "one" in front for proper format.
This eliminates a, d, e, i, l, n, o, q, r, and u
The letter "b" is not used yet so "billion" must be included, giving us only the b
Similarly the "m" is not used so "million" must be included
The new highest valued word that must be included is hundred which gives the "h"
a, b, d, e, h, i, l, m, n, o, q, r, and u  (13 letters)
The new highest is "twenty" giving the t, w, and y
Then an "eight" is needed for the g
a, b, d, e, g, h, i, l, m, n, o, q, r, t, u, w, and y (17 letters)
Then "six" for s and x
and lastly a "five" for f and v
a, b, d, e, f, g, h, i, l, m, n, o, q, r, s, t, u, v, w, x, and y (21 letters)

To make the number the lowest, it is easiest to place a one in front of quadrillion, billion and million and hundred.  However the twenty, eight, six and five, will have to fit amongst those words.

At first five-thousand, six-hundred twenty eight sounded good, but I realized the numbers could be changed to "two-thousand, five-hundred, sixty eight", and still have the same letters.

 

Posted by Leming on 2008-09-17 19:28:29