Amazing arrangement
I have 8 cue sticks and while playing with billiard balls in three dimension, a strange question struck me. What's the maximum number of cue sticks you can put in an arrangement so that each of them touches every other.
As I started trying arrangements in incremental order, I amazed myself everytime, so when did I stop ?
As I started trying arrangements in incremental order, I amazed myself everytime, so when did I stop ?
Labels: bcreative, out-of-the-box, thinktank
posted by Rajesh Lal at
9:48 AM
18 Comments:
8. all tips touching if youre playing in thre dimentions.
You can't have all tips touching each other. I think the intent is to have all sticks touching all sticks, not just touching one other stick (in which case the anser would be infinate).
I can easily get 6 touching by having three touch each other at the tips (laying flat, the middle of the three pulled back just enough to let the two outside sticks touch each other). Then laying three more stick on top of the first three, with a similar arrangement.
I think there's a better answer though.
*The top three are at a small angle off the first three, not directly on top of each other.
4
3 in two-dimension and 1 sticking up.
Originally I was going to answer was 5, but the two (one sticking down and the other sticking up) would not be touching each other.
So, I'm saying 4! I know with all of you 'logic' people out there, I'll probably add another "Duh" to my record but that's my story and I'm sticking to it.
when he ran out of ways duh XD
A simple "starburst" configuration, with each cue crossing the others in or near their middles, will allow all eight cues to be placed with each touching all others.
I would show you how, but my 3-D software is at work.
read the whole qustion it says, "when did i stop?" the answer to that is when he didnt have any more ways to connect them.
~lady~
who cares if it's 3 dimension if you can't do it in real life? the question says cue sticks for a reason, you can't balance a cue stick and let it touch other sticks. we're not in a circus. so I'm guessing the answer is 4, 3 making a triangle and a forth one touching two tips of two sticks and the middle of the third
like above but you could also place one paralell to the last cue on the other side of the triangle. what do you think?
That wouldn't work unless you threaded the fourth cue through the middle of the triangle and the last through from the opposite side.
As the question asks, he stopped when he ran out of cues.
I got 7.
make a triangle with them overlapping. then, put another one on the outside of each, then, put one vertically...oops, doesn't touch outside...er I got six!
Most of you are trying to answer the question that puzzled the guy/gal in the puzzle instead of answering the question in the puzzle which is when did he/she stop.
He stopped when he ran out ideas is my guess
You had the right idea. The question was when did he stop. He only had 8 cues, so I would assume he stopped at 8.
First you take one cue to use as your axle. You then form a triangle using two additional cues. Keep adding two cues and forming triangles all the way around the axle stick. I don't know how many sticks would physically fit into the formation, but in the end you would end up with a double-cone shape in which the bases meet. Theoretically hundreds of cues could be used, but since our man only had 8, I assume that's where he stopped.
ANSWER
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on the pool table you can have at the most 6 cue sticks arrangements such that each of them touches each other.
http://trickofmind.com/images/puzzles/6_stick_solution.gif
If you imagine in 3-D space you can have 7 sticks arrangement as shown in the picture
http://trickofmind.com/images/puzzles/7_stick_solution.gif
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2 possible answers..
"when did he stop"
a) when he ran out of positions that he could make them all touch ..
OR
b) her ran out of cue sticks
he stoped wen he brok one of the sticks........... lets reword that...
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