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Berry's Paradox


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#1 bonanova

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Posted 19 September 2007 - 09:42 AM

Considering only positive integers, 7 is unambiguously specified by the phrase the smallest number not specifiable using fewer than two syllables.

What is the smallest number not specifiable using fewer than twenty-three syllables?


Spoiler for Hint


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#2 Writersblock

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Posted 19 September 2007 - 10:31 PM

Possible
Using your prompt, 7,777,777 would make sense.
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#3 Scraff

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Posted 19 September 2007 - 10:45 PM

What does 'not specifiable' mean? Seven has two syllables. Eight has one. I'm obviously not getting something.
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#4 unreality

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Posted 20 September 2007 - 12:00 AM

"se-ven" is the only one digit number with more than one syllable... so you'll get more syllable per smaller number, so to speak
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#5 Scraff

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Posted 20 September 2007 - 12:14 AM

Possible
Using your prompt, 7,777,777 would make sense.


That has 24 syllables. 7,777,778 has 23. One trillion one has 4 syllables. I'm not gettin' it.
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#6 unreality

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Posted 20 September 2007 - 12:31 AM

this should clear it up:

the smallest number



we want the smallest number thats 23 syllables... so it would be 777,777,778 or whatever you said.
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#7 Ploper

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Posted 20 September 2007 - 01:08 AM

OH MY GOD!

23!
2/3 equals 0.666!
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#8 Scraff

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Posted 20 September 2007 - 03:15 AM

we want the smallest number thats 23 syllables


No, we don't. We want "the smallest number not specifiable (whatever that means) using fewer than twenty-three syllables".
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#9 Writersblock

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Posted 20 September 2007 - 05:39 AM

Exactly.

What is the smallest number not specifiable using fewer than twenty-three syllables



It's written kind of ambigously, but it means that the number must be:
specifiable
using MORE than 23 syllables and no less
the smallest such number to fit the definition

and from the prompt

Considering only positive integers



It must be a positive integer.

EDIT:

Even as I wrote this, I disagreed with myself.

not specifiable using fewer than twenty-three syllables


This would allow 23 syllables and therefore it would be 7,777,771.
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#10 Scraff

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Posted 20 September 2007 - 02:04 PM

It's written kind of ambigously, but it means that the number must be:
specifiable


The OP said, "not specifiable". And I still don't know what that means.


not specifiable using fewer than twenty-three syllables


This would allow 23 syllables and therefore it would be 7,777,771.


You're saying 23 is less than 23? 1 is less than 23. I think that would make the answer: 1. Although I'm not sure if the 'not specifiable' part cahanges the answer.
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