[wolfgang]

Hello dear friends....

Let me choose ten sticks for this puzzle

I I I I I I I I I I they should be in this start position

your aim is to make them doubles like this

X X X X X

you have to pick a stick and move it three steps ( to any direction )then put it on the 3rd stick ( any 2 sticks should be counted as 2). three sticks are not allowed.

for example: if you choose the 1st stick(to the left),then it should move to the right three steps(the stick itself will not be counted), so it will couple with No. 4 to be like this

I I X I I I I I I

have a nice time

[Guest]

Too lazy to write it, but the answer is to start from 5 pairs and work backwards...

This was once a Java puzzle on a Japanese puzzle site, man I wish I could find that site again...

[Guest]

IfIv understood this correctly, this is the solution I've come up with...

I I I I I I I I I I

I I I I I I I I X

I X I I I I I X

I X I I X I X

X X I X I X

X X X X X

This obviously works reflected as well (second line being X I I I I I I I I)

[Guest]

Not possible. 2047 is not a multiple of 9.

[Guest]

Realised my solution isnt that good visually

IfIv understood this correctly, this is the solution I've come up with...

I I I I I I I I I I

I I I I I I I I X

I X I I I I I X

I X I I X I X

X X I X I X

X X X X X

This obviously works reflected as well (second line being X I I I I I I I I)

new...

the dashes represent where the stick was moved from and the X is where it's moved to.

I've also added numbers in. The numbers are the original positions of the 10 sticks

I I I I I I I I I I

I I I I I I-I I X ::::::7 moves to 10

I X I I-I I I X ::::::5 moves to 2

I X-I I X I X ::::::3 moves to 8

-X X I X I X ::::::1 moves to 4

X X X X - X ::::::9 moves to 6

X X X X X

[Guest]

I I I I I I I I I I

I I I I I I-I I X ::::::7 moves to 10

I X I I-I I I X ::::::5 moves to 2

I X-I I X I X ::::::3 moves to 8

-X X I X I X ::::::1 moves to 4

X X X X - X ::::::9 moves to 6

X X X X X

You can't count moving over an empty space as a "step" when it is convenient (as, e.g. when you say "9 moves to 6"), and ignore it when it is not (as in "3 moves to 8").

Also, I've just realized that I don't quite understand the OP.

move it three steps ( to any direction )then put it on the 3rd stick ( any 2 sticks should be counted as 2).

seems to imply that moving the leftmost stick of |X| to the right results in XX (i.e. the original "X" is counted as two "steps". I assumed it would result in X|| (hopping over an "X" is one "step"). Either way there is no solution, but in the former case the proof is trivial: there is simply no legal move starting from XXXXX, so the inverse must also be true.

[Guest]

You can't count moving over an empty space as a "step" when it is convenient (as, e.g. when you say "9 moves to 6"), and ignore it when it is not (as in "3 moves to 8").

Also, I've just realized that I don't quite understand the OP.

seems to imply that moving the leftmost stick of |X| to the right results in XX (i.e. the original "X" is counted as two "steps". I assumed it would result in X|| (hopping over an "X" is one "step"). Either way there is no solution, but in the former case the proof is trivial: there is simply no legal move starting from XXXXX, so the inverse must also be true.

It all depends on what is meant by a step.

-If it means that the 10 spaces are maintained throughout and stick can jump into the blank spaces then my solution does not work.

-If it means that you jump over the next stick(s) and ignore the blank spaces left then it does work:

when it is said

( any 2 sticks should be counted as 2).

then I assumed that everytime you try to jump over a cross you count 2, not 1.

so I X I

would become X X (the first stick jumps over the cross counts as 2 and then and lands on the third stick to cross it)

[Guest]

^ I think these are the rules:

You have ten sicks, your objective is to make them 5 pairs.

Each stick must jump over exactly two sticks and combine with the third one, a combined pair will count as two sticks.

This is solvable...

[Guest]

there is simply no legal move starting from XXXXX, so the inverse must also be true.

^ Er, oops. That's actually not true.

[wolfgang]

It all depends on what is meant by a step.

-If it means that the 10 spaces are maintained throughout and stick can jump into the blank spaces then my solution does not work.

-If it means that you jump over the next stick(s) and ignore the blank spaces left then it does work:

when it is said then I assumed that everytime you try to jump over a cross you count 2, not 1.

so I X I

would become X X (the first stick jumps over the cross counts as 2 and then and lands on the third stick to cross it)

yes...you did it!....we should ignore blank spaces....your above answer was right!!