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7 replies to this topic

#1 itachi-san

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Posted 26 May 2008 - 05:34 PM

Usually hand-written stars are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA. The segments must always alternate a constant number of points (in the above case, skipping 1 point in between).

Given the following info:
1)there is only 1 way to draw a 5-point star
2)there is NO way to draw a 6-point star (in continuous lines, that is)
3)there are 2 ways to draw a 7-point star

how many different ways are there to draw a 1000-point star?
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#2 Georgie

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Posted 26 May 2008 - 05:39 PM

Spoiler for not sure but...

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#3 octopuppy

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Posted 26 May 2008 - 05:44 PM

Spoiler for I make it..

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#4 itachi-san

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Posted 26 May 2008 - 05:46 PM

Spoiler for I make it..

Yep. Good job
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#5 Budouka

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Posted 27 May 2008 - 10:14 PM

Pardon me, but I'm missing something here; maybe it's an incorrect assumption on my part. If you are drawing a star with continuous line segments, isn't there only one way to draw any given star, unless you count stroke direction, in which case there are two ways for stars with odd-numbered points and still no ways (line segments cannot be continuous) for stars with even points? What am I missing?
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#6 flowstoneknight

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Posted 27 May 2008 - 10:24 PM

Pardon me, but I'm missing something here; maybe it's an incorrect assumption on my part. If you are drawing a star with continuous line segments, isn't there only one way to draw any given star, unless you count stroke direction, in which case there are two ways for stars with odd-numbered points and still no ways (line segments cannot be continuous) for stars with even points? What am I missing?


You can test this out yourself. Draw seven points evenly spaced on a circle. Starting at any point, draw a line to the next next point (so you're skipping one). Keep doing this until you've drawn a star. Now draw the same seven points, but this time skip two points when connecting them (so connect it to the next next next point). You'll see that you've drawn a different star. There are many different stars to be drawn for other numbers.
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#7 Budouka

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Posted 27 May 2008 - 10:38 PM

Thanks, flowstone, I get it now. That's pretty cool.
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#8 woon

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Posted 30 May 2008 - 10:32 AM

Spoiler for I am not sure, but I guess...

Edited by woon, 30 May 2008 - 10:37 AM.

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