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Puzzles / Riddles:  Star and Stone

Posted on 2008-06-18
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Last Modified: 2011-10-19
My friend has given me a riddle to solve and I feel that the solution is already somewhere in the internet. I would be happy to know the link.

Riddle:
1) Draw a Star. It will have 10 points.
2) Take 9 stone.
3) From a blank point count 1,2,3 and at 3rd point place the stone.
4) You are allowed to jump over 1 stone and not more than one stone.
5) Such way all 9 stones will be placed at 9 points of the star and one point will remain blank

Riddle By Mat
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Question by:Mehram
  • 10
  • 10
  • 9
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Expert Comment

by:ozo
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At least one interpretation of those 5 statements could give
          1

3     9    6     4
   
      7      8
          b

   5              2
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by:Infinity08
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>> 3) From a blank point count 1,2,3 and at 3rd point place the stone.

Can you clarify this ... Can you move in any direction (clockwise, counterclockwise) ?


>> 4) You are allowed to jump over 1 stone and not more than one stone.

Does the jump count as part of the 3 positions you skip ?


>> 5) Such way all 9 stones will be placed at 9 points of the star and one point will remain blank

I assume that the question is which remains blank ?
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Expert Comment

by:Infinity08
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>> >> 4) You are allowed to jump over 1 stone and not more than one stone.
>>
>> Does the jump count as part of the 3 positions you skip ?

Oh, and can you jump one stone more than once during a move ?
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Author Comment

by:Mehram
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>> 3) From a blank point count 1,2,3 and at 3rd point place the stone.

Can you clarify this ... Can you move in any direction (clockwise, counterclockwise) ?
straight line back and forth

>> 4) You are allowed to jump over 1 stone and not more than one stone.

Does the jump count as part of the 3 positions you skip ?
Yes it counts.

>> 5) Such way all 9 stones will be placed at 9 points of the star and one point will remain blank.
Any one of the 10 point will remain blank.

I assume that the question is which remains blank ?
No. The question is how to place stone fulfilling all rule. In practice, When I try I am stuck at some point like there are two stones placed continuously and I cant continue further
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by:ozo
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> straight line back and forth
If you can go back and forth, and the jump over one stone counts as part of the 3 positions you skio,
then each stone after the first can start behind the previous stone 1, jump onto the previous stone 2 and back to where it started 3
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Expert Comment

by:Infinity08
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>> straight line back and forth

So, you don't have to follow the contours of the star ?

Does the starting point count as one of the 3 positions you skip ?
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Author Comment

by:Mehram
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Does the starting point count as one of the 3 positions you skip ?
Yes.

<<3 positions you skip ?>>
Note, the count ends on 3 not 2.  So one skip two positions, not three positions.
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Expert Comment

by:ozo
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> Note, the count ends on 3 not 2.  So one skip two positions, not three positions.
So you start at 0, skip 1, skip 2, and end on 3?
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Author Comment

by:Mehram
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<<3 positions you skip ?>>
Note, the count ends on 3 not 2.  So one skip two positions, not three positions
I was wrong.
Start count =1
end count = 3
One cannot skip more than one position.

So Ozo you are right, but

> Note, the count ends on 3 not 2.  So one skip two positions, not three positions.
So you start at 0, skip 1, skip 2, and end on 3?
No,
I start at 1,skip 2 and end on 3
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Author Comment

by:Mehram
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Hi ozo, AND ALL EXPERT THIS SHOULD MAKE THE RIDDLE EXTREMELY CLEAR

From any blank positon
I START AT 1, SKIP 1 ( IF A STONE IS PLACED THERE) END ON 3
WHEN ALL POINTS ARE BLANK THEN
I START AT 1, COUNT 2 AND END ON 3

IF TWO STONES ARE PLACED TOGETHER, THEN
FROM ANY BLANK POSITION
I START AT 1 AND THEN STUCK AS TWO STONES ARE PLACED TOGETHER.


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Expert Comment

by:Infinity08
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>> So, you don't have to follow the contours of the star ?

Let's make it clear with an example.

Below is a star with the points marked by letters. From point a, where can I move to ? (assuming that no stones have been placed yet)
star.png
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Author Comment

by:Mehram
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Hi infinity08
Your star shape is not as mine. Wait, I am painting in note pad.
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Expert Comment

by:ozo
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If the 10 points form a circle or a line, rather than a star graph like
http://mathworld.wolfram.com/images/eps-gif/MagicPentagon_1000.gif
then you can color alternate ponts red and black so that each step is from red to black
or black to red. and a start at 1 is the same color as an end on 3
If you want to end with a single empty point, say a black one,
and if the start point at 1 can't be the same as the endpoint at 3,
(so that you don't go "back and forth")
then the last stone to be placed must have started in that open black point, and ended at another black point.
which means that before the last stone was placed there were two open black points.
then the next to last stone to be placed must have started in one of those open black points and ended at another black point.
which means that before the next last stone was placed there were three open black points.
...
which means you could never have filed in a white point.

Was one of the rules misunderstood?
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Author Comment

by:Mehram
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The shape of the star with 10 points marked by bold dot. Saved into star.bmp
star.bmp
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Author Comment

by:Mehram
Comment Utility
Hi ozo,

You have got my shape and idea. However, I am unable to understand the logic.
Can you make it more clear for me. Or
Can you place the stone one by one in 9 steps and give me the picture.

First step, picture will have one stone.
Second Step, picture will have two stones
.....
....
Ninth step , picture will have 9 stones and one point will be blank.
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Expert Comment

by:Infinity08
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So, a revised image with lines added. So, from a, where can we get to ?
star2.png
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Expert Comment

by:Infinity08
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What about the order a -> c -> e -> g -> i -> b -> f -> j -> d -> h ? Is that valid ?
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Expert Comment

by:Infinity08
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Or can it only be in straight lines ? In that case :

a -> d -> g -> j -> c -> f -> i -> b -> e -> h
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Expert Comment

by:ozo
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With the pentagram graph, if a count be between any two points joined by an edge, then placing
the stones in the order suggested in http:#a21819506 (with the final blank point at b)
seems to follow all the rules.
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Expert Comment

by:Infinity08
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>> seems to follow all the rules.

Except the new one :

>> I START AT 1, COUNT 2 AND END ON 3

if I'm not mistaken ...
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Accepted Solution

by:
ozo earned 250 total points
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If the count from 1 to 2 must be colinear with the count from 2 to 3, then
filling stones int the order
b->d->e
i->j->b
f->h->i
c->d->f
j->b->c
g->h->j
d->f->g
a->b->d
h->j->a
seems to follow all the rules
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Expert Comment

by:Infinity08
Comment Utility
which is the same order I posted here : http:#21820216 ;)
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Author Comment

by:Mehram
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Hi experts,
I am seeing all the comments, I would accept, after I have tried the answer.
Because right now, I am in the office.
Wait till tomorrow
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Expert Comment

by:ozo
Comment Utility
You don't have stones or stars in the office?
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Author Comment

by:Mehram
Comment Utility
Hi ozo
<<You don't have stones or stars in the office?>>
I take back my previous comment and apologise.

Your answer
b->d->e
i->j->b
f->h->i
c->d->f
j->b->c
g->h->j
d->f->g
a->b->d
h->j->a
ABSOLUTELY CORRECT.

Infinity 08 is saying it is same as
a -> d -> g -> j -> c -> f -> i -> b -> e -> h
I am not intelligent enough to understand how it is same.

Infiniy08, Either u clear me, or Ozo confirm your statement then I would accept your and ozos answer.


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Assisted Solution

by:Infinity08
Infinity08 earned 250 total points
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>> I am not intelligent enough to understand how it is same.

Start at position a, then move to position d (through b), then to g (through f), etc. The stones are put on these positions in this order :

        a -> d -> g -> j -> c -> f -> i -> b -> e -> h

Formatting it the same way ozo did, you'd get :

e -> f -> h
b -> d -> e
i -> j -> b
f -> h -> i
c -> d -> f
j -> b -> c
g -> h -> j
d -> f -> g
a -> b -> d

Notice that the only difference is the starting point ...
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Expert Comment

by:ozo
Comment Utility
Infinity08 probably meant for you to break it up as
a -> d -> g -> j -> c -> f -> i -> [b -> e -> h]
a -> d -> g -> j-> c -> f -> [i -> b -> e] -> h
a -> d -> g -> j -> c -> [f -> i -> b] -> e -> h
...
Similarly, Infinity08's first answer appears to be essentially the same as my first answer if you are allowed to follow any line,
where I just listed the final positions of each stone, without specifying how it got there.

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Expert Comment

by:ozo
Comment Utility
> Infinity08 probably meant for you to break it up as
I guess not.  I should have referred back to the picture to see how the notation related to the connections
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Author Closing Comment

by:Mehram
Comment Utility
Want to be remembered in your good name
Thanks
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