# checkers puzzle

• Sep 15th 2006, 09:13 AM
samsum
checkers puzzle
Ten checkers numbered 1 – 10 are lined up as shown in the figure below. Your objective is to create five piles of two checkers each in only five moves. On each move a single checker must “jump” exactly two checkers (in either direction) and land on the next single checker. The two jumped checkers may be two single checkers side-by-side or a stacked pair.

Hints:

Try to use 10 pennies represent checker 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

examples: checker 1 was on top checkers 3 and so on.....

Have fun with it.

I think this will help you to solve it, thanks for interested in. :)
• Sep 15th 2006, 09:18 AM
CaptainBlack
Quote:

Originally Posted by samsum
Ten checkers numbered 1 – 10 are lined up as shown in the figure below. Your objective is to create five piles of two checkers each in only five moves. On each move a single checker must “jump” exactly two checkers (in either direction) and land on the next single checker. The two jumped checkers may be two single checkers side-by-side or a stacked pair.

Hints:

Try to use 10 pennies represent checker 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

examples: checker 1 was on top checkers 3 and so on.....

Have fun with it.

A bit difficult without the figure.

You can upload the figure using the Manage Attachments dialogue on
the edit window (choose the advanced editing option and scroll down)

RonL
• Sep 17th 2006, 04:46 PM
samsum
Quote:

Originally Posted by CaptainBlack
A bit difficult without the figure.

You can upload the figure using the Manage Attachments dialogue on
the edit window (choose the advanced editing option and scroll down)

RonL

yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.
• Sep 17th 2006, 04:52 PM
dan
i can't even understand the problem...:(
• Sep 17th 2006, 09:09 PM
CaptainBlack
Quote:

Originally Posted by samsum
yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.

Don't quote me, in order to make some point not related
to my post.

RonL
• Sep 19th 2006, 11:55 AM
CaptainBlack
Quote:

Originally Posted by samsum
yeah, it is so difficult to figure out how to solve it. If is easy, it won't be a puzzle.

and will you cut us in on the prize if we solve this for you?

RonL
• Sep 20th 2006, 10:36 PM
CaptainBlack
I will unlock this thread on the 1st of October (assuming I remember), and
if there are no correct solutions within 24 hours I will post one of the solutions.

Gratis clue: the gaps left by checkers that have jumped are not significant
and are to be treated as though they are not there.

RonL
• Sep 25th 2006, 12:26 PM
CaptainBlack
I have reopened this early as I may not be around to do this
when I said I would.

This is a variant of the eight coins problem.

1. Start by jumping checker 7 over 8 and 9 onto 10.

Now we are left with an eight checker problem with checkers 1, 2, 3, 4,
5, 6, 8, 9
.
2. jump 4 over 5&6 onto 8
3. jump 6 over 5&3 onto 2
4. jump 3 over stack with 6&2 onto 1
5. jump 5 over stack with 4&8 onto 9.

(note the gaps between checkers left by jumps are ignored for subsequent
moves)

This generalises to any even number of checkers >=8. It is fairly easy
to show that there is no solution for 6 or fewer checker.

RonL
• Sep 25th 2006, 08:12 PM
samsum
Is that so simple ?
my solution is:

step 1: let checker 7 jumps over 8 & 9 onto 10
1 , 2, 3, 4, 5, 6, 8, 9, 7/10
step2: jump checker 5 over 3 & 4 onto 2
1, 5/2, 3, 4, 6, 8, 9, 7/10
step 3: jump 3 over 4 & 6 onto 8
1, 5/2, 4, 6, 3/8, 9, 7/10
step 4: jump 9 over 3/8 onto 6
1, 5/2, 4, 9/6, 3/8, 7/10
step 5: the last move will jump the checker 1 over 5/2 onto 4.

I hope this will be the same as yours. No arguments huh ? Let's others opinions. Thanks anyways Captainblack.