Coin Puzzle

[Judd]

OK so it isn't strictly (but it could be!) maths, but this seems to be
the place for curious puzzles.

It might help to place five coins (three of one type, two of
another) in a line on the table.

Can you rearrange the following:

xoxox
to
xxxoo

subject to the following rules:

1) You must move two adjacent red and black coins each time.
2) Each move must 'jump' at least one other adjacent
coin (i.e. you are not allowed to 'jump' spaces).

This can be done in five moves - persistence will pay off :)

[kedaman]

how do you move them and what's jump? (give me example)

[Judd]

OK,

A move consists of (for example):


xoxox ----> xoxxo


If you're doing this with real coins a move consists of putting two
fingers of one hand on the relevant coins and sliding them on
the table to the new poistion.

Jumping is a little harder to explain, but is quite easy once you
get it. In the above example the black coins (xox) are initially
adjacent to the moved coins and are 'jumped' (i.e., when sliding
the blue coins you move them 'over' the black coins).

If you have the following situation (an dash represents a 'coin space'):


oxx--xo


You are not allowed to move the two right most coins either into
the space (not jumping an adjacent coin) or to the LHS of the row
(jumping the space). You are allowed to move the two left most
coins into the space (jumping the adjacent x), but not to
the RHS of the row (jumping the space).

Perhaps I got the explanation wrong above:

You can never jump a space, but you must jump
at least one coin which is initially adjacent to the coins being moved.

Hope you can understand that, if not, reply back and I'll try to
explain more.

[kedaman]

So, when i move two coins their place is replaced by blanks, and I can only move coins to blank spaces, am I right? Or is it allowed to do insertion, which means coins will be shifted forward or backwards to open space for the movement?

[Starman]

I can do it in 3 moves.

[Judd]

kedaman: if I understand you correctly, yes you are only allowed to move into blank spaces (which may be on the end of the row of coins), no you are not allowed to 'insert' (you must jump at least one coin with each move). Try to imagine (or get some coins and really try it!) how you would make the moves in reality - five coins in a row, place the fisrt two fingers of you preferred hand on two of the coins, slide them on the table top...that is the only type of move you can make -only two fingers on two coins at any time.


starman: if you can do it in three moves, please demonstrate :p


I would suggest something like the following to indicate moves in this forum:


Move 1:
|-|-|x|o|x|o|x|-|-|
|-|-|-|-|x|o|x|x|o|


where |-| indicates a blank space, the blue coins are the start of the move, the red coins their final position.

[Starman]

|-|-|x|o|x|o|x|
|x|o|x|o|-|-|x|
|x|-|-|o|o|x|x|
|x|x|x|o|o|-|-|

sorry, colours are a bit beyond me, but I think you can see the moves.

They do end up shifted left by two places, is this legal ?

[Judd]

They do end up shifted left by two places, is this legal ?
Yes.

But in your final move you are moving two 'x' coins.

From my first post:

1) You must move two adjacent red and black coins each time.
or in your case, 'x' and 'o'.

[color=red]If I removed the space after the slash, this text would be red[/ color]

[Starman]

oops! missed that instruction.
I'll try again.

[kedaman]

x o x o x _ _
_ _ x o x x o _ _
_ _ _ _ x x o x o
_ _ _ _ x _ _ x o x o
_ _ _ _ x o x x _ _ o
_ _ _ _ _ _ x x x o o

[rplcmint]

From what I understand from the instructions..I can do it in two moves.

[Judd]

Kedaman's solution is correct, at least the way I interpretted the rules.

If you can do it in two moves - please back your claim with a demonstration....

:)