perplexus.info :: Numbers : It isn't a kajillion zillion! II

It isn't a kajillion zillion! II (Posted on 2008-09-28)

For the following, only letters unique to the spelling of the American English constructed name of the cardinal number shall be counted in determining the length of the cardinal number. Spaces, hyphens and commas are also excluded in determining length. For example, SEVEN has a length of 3 as the E occurs more than once in it spelling. Also note, in American English, the occurance of the connecting word 'and' is ommitted in the construction of a cardinal number's name.

1. What is the largest cardinal number of greatest length?

2. What is the smallest cardinal number of shortest length?

Submitted by Dej Mar

Rating: 5.0000 (1 votes)

Solution: (Hide)

The largest I've discovered, with the currently accepted names, is:
99,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,019,000,019,019,000,019,000,018,005,000,002
[ninety-nine centillion, nineteen nonillion, nineteen septillion, nineteen sextillion, nineteen quadrillion, eighteen billion, five million two] with an effective length of 16 (YCPXQUADRGHBFVMW). As almost all base names greater than 10³ will have the numeric suffix -illion (the exception is google and googleplex), the I, L, N and O, along with the letters E and T, can be allowed to occur as often as needed in order to add the letters A, B, C, D, P, Q and U which do not occur uniquely in any cardinal number less than 10³.

The smallest is 3,000,000,000,404 [three trillion four hundred four] with an effective length of 0, having all letters in its construction discounted.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-04-19 23:59:30
. . . and an end for Part 1.	Leming	2008-09-28 21:33:24
re: Just a start	Leming	2008-09-28 20:34:35
Just a start	Leming	2008-09-28 20:24:08
Part 2 . . . (Spoiler)	Leming	2008-09-28 20:19:47

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