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        riddles >> medium >> Slash 'n' Dash Sequence
        
(Message started by: Jeremiah Smith on Jan 31^st, 2003, 9:30am)

Title: Slash 'n' Dash Sequence
Post by Jeremiah Smith on Jan 31^st, 2003, 9:30am

What are the next few terms in this sequence?

-
/-\
/-\-
//-\\
/-\--
/-\/-\
/-\---
///-\\\
//-\\-
/-\-/-\

Hint: [hide] Maybe it'll go easier if you replace - with 0, and the / and \ with ( and ). Or not. [/hide]

Hint: [hide] These are just the numbers 1 through 10, expressed differently. And despite the presence of zero, you can't express zero this way.[/hide]

Hint: [hide] All your base are belong to prime numbers. [/hide]

Title: Re: Slash 'n' Dash Sequence
Post by Phil on Jan 31^st, 2003, 1:27pm

I had to make use of all of your hints to get this answer:[hide]
/-\----
/-\//-\\
/-\-----
/-\--/-\
/-\/-\-
////-\\\\
/-\------
//-\\/-\
/-\-------
/-\-//-\\ [/hide]

Title: Re: Slash 'n' Dash Sequence
Post by Disoriented on Mar 27^th, 2003, 1:34pm

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. ???

Title: Re: Slash 'n' Dash Sequence
Post by Oriented on Mar 27^th, 2003, 2:35pm

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
/-\//-\\-//-\\