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Topic: Slash 'n' Dash Sequence (Read 1904 times) |
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Jeremiah Smith
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Beep!
Posts: 172
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Slash 'n' Dash Sequence
« on: Jan 31st, 2003, 9:30am » |
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What are the next few terms in this sequence?
-
/-\
/-\-
//-\\
/-\--
/-\/-\
/-\---
///-\\\
//-\\-
/-\-/-\
Hint: Maybe it'll go easier if you replace - with 0, and the / and \ with ( and ). Or not.
Hint: These are just the numbers 1 through 10, expressed differently. And despite the presence of zero, you can't express zero this way.
Hint: All your base are belong to prime numbers.
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| « Last Edit: Jan 31st, 2003, 9:32am by Jeremiah Smith » |
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Phil
Newbie
Posts: 38
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Re: Slash 'n' Dash Sequence
« Reply #1 on: Jan 31st, 2003, 1:27pm » |
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I had to make use of all of your hints to get this answer:
/-\----
/-\//-\\
/-\-----
/-\--/-\
/-\/-\-
////-\\\\
/-\------
//-\\/-\
/-\-------
/-\-//-\\
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Disoriented
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Re: Slash 'n' Dash Sequence
« Reply #2 on: Mar 27th, 2003, 1:34pm » |
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I guess I'm still not clear. So far, I've been able to see the following patterns.
- Every power of 2 is of the form ///.../-\...\\\
- Every prime number is of the form /-\---...-
But I'm still not sure how to derive non primes and non-powers of two. 
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Oriented
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Re: Slash 'n' Dash Sequence
« Reply #3 on: Mar 27th, 2003, 2:35pm » |
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A number is represented by factoring it. For any given number, the rightmost digit (-,/-\,//-\\,///-\\\...)gives you the power of 2 that is a factor. The second digit counts 3's. THird digit is 5's. So, for example 700 would be
7^1 * 5^2 * 3^0 * 2^2
represented as
1202
or
/-\//-\\-//-\\
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