[Guest]

Been a while since I've been on, but thought I'd share this puzzler:

(hope it hasn't been on here before)

What is the largest positive interger that describes the number of letters in that interger when written in english?

[unreality]

Good to see you back!

FOUR

[bonanova]

Hey ... ltns

something in the teens, but I got tired of looking past 20.

Can it simply be four?

[Guest]

Edit..

** Sorry wrong one! **

Edited October 13, 2008 by JarZe

[Prime]

What about...

INFINITY.

I mean if one tried to really write it out.

Or some other recursive solutions:

"The integer describing number of letters required to write out an infinite positive integer in English."

Or more to the point:

"The largest positive interger that describes the number of letters in self when written in english."

[Guest]

It is, in fact, F-O-U-R. And as far as I can tell, this is the ONLY self-referential postitive interger that fits the puzzle. Once you get over 10 or 11, you are getting into very large words. It doesn't help to add more "words" to the number either, as the difference between 20 and 120 is far greater in numbers than in letters spelling "Twenty" versus "One Hundred Twenty." Therefore you are forced to look to ever smaller numbers to get a 1to1 relationship between value and number of letters, with 4 being the simple and only answer.

Infnity isn't going to work because of the same concept above. Once you hit One Hundred you are hoplessly lost, as the ratio is 1:10 (ten letters to define 100 units). Therefore any number greater than one hundred will have this same flaw. (One million, or billion, or trillion only digs deeper and deeper holes).

Here's a related puzzle that just occurred to me:

What is the least number of letters you can use to express an amount greater than the number of letters in the word?

For example, Seven expresses an amount greater than the number of letters: 5 letters, 7 units. But "one" doesn't work = 3 letters, 1 unit.

[Izzy]

3 letters. It's true for SIX and TEN.

[Guest]

I'd propose you don't have the right answer yet.

[Guest]

Something like

pi (2 letters 3.14159...units) or

e (1 letter 2.71828 units)

Unless the same rules as the first puzzle apply, though this was not specifically mentioned.

Edited October 22, 2008 by Mac The Cat

[Guest]

the second question

googel (1*10^100)

[Guest]

Mac got what I had in mind. Mathmatical constants that are referenced by a letter, though you have to spell out the letter. Not sure about "e" but, Pi certainly works.

Not deep, but interesting to me...

[Guest]

You could also use roman numerals, X V or anything bigger than I would work.

[Guest]

So what would be the greatest amount referenced by the smallest number of letters, not counting infinity?

Meaning to get the answer correct, your answer must have the smallest number of letters first, then be the highest amount using that number of letters. Single letters don't count, so is Pi the answer?

[Guest]

So what would be the greatest amount referenced by the smallest number of letters, not counting infinity?

Meaning to get the answer correct, your answer must have the smallest number of letters first, then be the highest amount using that number of letters. Single letters don't count, so is Pi the answer?

If you do count Roman numerals, wouldn't it be MMM (a difference of 2997?)

[Guest]

I'd plumb for the Avagadro constant symbolised by L or N_A

1 (or two) letters with a value of 6.022 x 10²³

[Guest]

In my usage, the "letters" have to form a "word," or in other words, it needs to be able to be "spelled out" in english to fit. Therefore Roman numerals and single letter constant symbols don't work unless you spell out the words.

[Guest]

Been a while since I've been on, but thought I'd share this puzzler:

(hope it hasn't been on here before)

What is the largest positive interger that describes the number of letters in that interger when written in english?

TWENTY NINE

count the strokes to write it -

[Guest]

It is, in fact, F-O-U-R. And as far as I can tell, this is the ONLY self-referential postitive interger that fits the puzzle. Once you get over 10 or 11, you are getting into very large words. It doesn't help to add more "words" to the number either, as the difference between 20 and 120 is far greater in numbers than in letters spelling "Twenty" versus "One Hundred Twenty." Therefore you are forced to look to ever smaller numbers to get a 1to1 relationship between value and number of letters, with 4 being the simple and only answer.

Infnity isn't going to work because of the same concept above. Once you hit One Hundred you are hoplessly lost, as the ratio is 1:10 (ten letters to define 100 units). Therefore any number greater than one hundred will have this same flaw. (One million, or billion, or trillion only digs deeper and deeper holes).

Here's a related puzzle that just occurred to me:

What is the least number of letters you can use to express an amount greater than the number of letters in the word?

For example, Seven expresses an amount greater than the number of letters: 5 letters, 7 units. But "one" doesn't work = 3 letters, 1 unit.

Seven only uses 4 letters. It's five long but only uses 4. Not sure if this train of thought gives more solutions to previous puzzle.

Edited October 31, 2008 by Pugster

[Guest]

Well then Avagadro's constant will still win, 17 letter to 6.022 x 10^23.

Or then infinity 8 letters infinite units.

Edited November 7, 2008 by Ventum