HereWeGoAgain
Grandpa
Or at least, score "genius" level on the peg jump game (as seen at Cracker Barrel restaurants).
Here is a solution that ends with one peg in the original open space. In the diagrams, 1 represents a peg, 0 represents an empty hole. Each jump is represented by taking the red peg and jumping it over the green peg into the blue hole (the green peg is then removed).
<span style='font-family: Courier New'>
(1)-------- (2)--------
-----<span style="color: #3333FF">0</span>----- -----1-----
----1-<span style="color: #33CC00">1</span>---- ----1-0----
---1-1-<span style="color: #FF0000">1</span>--- ---<span style="color: #FF0000">1</span>-<span style="color: #33CC00">1</span>-<span style="color: #3333FF">0</span>---
--1-1-1-1-- --1-1-1-1--
-1-1-1-1-1- -1-1-1-1-1-
(3)-------- (4)--------
-----1----- -----1-----
----1-0---- ----1-0----
---0-<span style="color: #3333FF">0</span>-1--- ---0-1-1---
--1-1-<span style="color: #33CC00">1</span>-1-- --1-1-0-1--
-1-1-1-<span style="color: #FF0000">1</span>-1- -1-<span style="color: #FF0000">1</span>-<span style="color: #33CC00">1</span>-<span style="color: #3333FF">0</span>-1-
(5)-------- (6)--------
-----1----- -----1-----
----1-0---- ----1-0----
---0-1-1--- ---<span style="color: #3333FF">0</span>-1-1---
--1-1-0-1-- --<span style="color: #33CC00">1</span>-1-0-1--
-1-0-<span style="color: #3333FF">0</span>-<span style="color: #33CC00">1</span>-<span style="color: #FF0000">1</span>- -<span style="color: #FF0000">1</span>-0-1-0-0-
(7)-------- (8)--------
-----1----- -----1-----
----<span style="color: #FF0000">1</span>-0---- ----0-0----
---<span style="color: #33CC00">1</span>-1-1--- ---<span style="color: #3333FF">0</span>-1-1---
--<span style="color: #3333FF">0</span>-1-0-1-- --1-<span style="color: #33CC00">1</span>-0-1--
-0-0-1-0-0- -0-0-<span style="color: #FF0000">1</span>-0-0-
(9)-------- (10)-------
-----1----- -----<span style="color: #FF0000">1</span>-----
----0-<span style="color: #3333FF">0</span>---- ----0-<span style="color: #33CC00">1</span>----
---1-1-<span style="color: #33CC00">1</span>--- ---1-1-<span style="color: #3333FF">0</span>---
--1-0-0-<span style="color: #FF0000">1</span>-- --1-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-
(11)------- (12)-------
-----0----- -----0-----
----<span style="color: #3333FF">0</span>-0---- ----1-0----
---<span style="color: #33CC00">1</span>-1-1--- ---<span style="color: #3333FF">0</span>-<span style="color: #33CC00">1</span>-<span style="color: #FF0000">1</span>---
--<span style="color: #FF0000">1</span>-0-0-0-- --0-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-
(13)------- (14)-------
-----<span style="color: #3366FF">0</span>----- -----1-----
----<span style="color: #33CC00">1</span>-0---- ----0-0----
---<span style="color: #FF0000">1</span>-0-0--- ---0-0-0---
--0-0-0-0-- --0-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-</span>
Here is a solution that ends with one peg in the original open space. In the diagrams, 1 represents a peg, 0 represents an empty hole. Each jump is represented by taking the red peg and jumping it over the green peg into the blue hole (the green peg is then removed).
<span style='font-family: Courier New'>
(1)-------- (2)--------
-----<span style="color: #3333FF">0</span>----- -----1-----
----1-<span style="color: #33CC00">1</span>---- ----1-0----
---1-1-<span style="color: #FF0000">1</span>--- ---<span style="color: #FF0000">1</span>-<span style="color: #33CC00">1</span>-<span style="color: #3333FF">0</span>---
--1-1-1-1-- --1-1-1-1--
-1-1-1-1-1- -1-1-1-1-1-
(3)-------- (4)--------
-----1----- -----1-----
----1-0---- ----1-0----
---0-<span style="color: #3333FF">0</span>-1--- ---0-1-1---
--1-1-<span style="color: #33CC00">1</span>-1-- --1-1-0-1--
-1-1-1-<span style="color: #FF0000">1</span>-1- -1-<span style="color: #FF0000">1</span>-<span style="color: #33CC00">1</span>-<span style="color: #3333FF">0</span>-1-
(5)-------- (6)--------
-----1----- -----1-----
----1-0---- ----1-0----
---0-1-1--- ---<span style="color: #3333FF">0</span>-1-1---
--1-1-0-1-- --<span style="color: #33CC00">1</span>-1-0-1--
-1-0-<span style="color: #3333FF">0</span>-<span style="color: #33CC00">1</span>-<span style="color: #FF0000">1</span>- -<span style="color: #FF0000">1</span>-0-1-0-0-
(7)-------- (8)--------
-----1----- -----1-----
----<span style="color: #FF0000">1</span>-0---- ----0-0----
---<span style="color: #33CC00">1</span>-1-1--- ---<span style="color: #3333FF">0</span>-1-1---
--<span style="color: #3333FF">0</span>-1-0-1-- --1-<span style="color: #33CC00">1</span>-0-1--
-0-0-1-0-0- -0-0-<span style="color: #FF0000">1</span>-0-0-
(9)-------- (10)-------
-----1----- -----<span style="color: #FF0000">1</span>-----
----0-<span style="color: #3333FF">0</span>---- ----0-<span style="color: #33CC00">1</span>----
---1-1-<span style="color: #33CC00">1</span>--- ---1-1-<span style="color: #3333FF">0</span>---
--1-0-0-<span style="color: #FF0000">1</span>-- --1-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-
(11)------- (12)-------
-----0----- -----0-----
----<span style="color: #3333FF">0</span>-0---- ----1-0----
---<span style="color: #33CC00">1</span>-1-1--- ---<span style="color: #3333FF">0</span>-<span style="color: #33CC00">1</span>-<span style="color: #FF0000">1</span>---
--<span style="color: #FF0000">1</span>-0-0-0-- --0-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-
(13)------- (14)-------
-----<span style="color: #3366FF">0</span>----- -----1-----
----<span style="color: #33CC00">1</span>-0---- ----0-0----
---<span style="color: #FF0000">1</span>-0-0--- ---0-0-0---
--0-0-0-0-- --0-0-0-0--
-0-0-0-0-0- -0-0-0-0-0-</span>