1. ## Classic Peg-Jumping Puzzle

A Classic Peg-Jumping Puzzle

There are four red pegs and four blue pegs as shown below.
There is an empty "hole" in the center.

Object: switch the positions of the red and blue pegs.

$\displaystyle \begin{array}{ccccccccc} {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} }\end{array}$

A peg can move into an adjacent hole
or jump a peg of opposite color.

Red pegs must move to the right.
Blue pegs must move to the left.

Good Luck!

2. ## Solution

Solution

$\displaystyle \begin{array}{ccccccccc}\\ {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} } \\ 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ \end{array}$

Note that the positions are numbered, not the pegs.

In the solution, a number is given for a move.
You will find that the peg at that position
has exactly one legal move.

Spoiler:

$\displaystyle \begin{array}{c} \text{4 - 6} \\ \text{7 - 5 - 3} \\ \text{2 - 4 - 6 - 8} \\ \text{9 - 7 - 5 - 3 - 1} \\ \text{2 - 4 - 6 - 8} \\ \text{7 - 5 - 3} \\ \text{4 - 6} \\ \text{5} \end{array}$

3. ## Need some help

How do you solve this?

Originally Posted by Soroban
A Classic Peg-Jumping Puzzle

There are four red pegs and four blue pegs as shown below.
There is an empty "hole" in the center.

Object: switch the positions of the red and blue pegs.

$\displaystyle \begin{array}{ccccccccc} {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & {\color{red}\boxed{\;}} & _{\_\_\_} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;}} & {\color{blue}\boxed{\;} }\end{array}$

A peg can move into an adjacent hole
or jump a peg of opposite color.

Red pegs must move to the right.
Blue pegs must move to the left.

Good Luck!

4. Thank you very much.