### Cracker Barrel Peg Puzzle (Projects)

When advancing our nefarious plans for World Domination requires us to travel,
we often take our meals at one of the many Cracker Barrel
restaurants. We particularly like their biscuits, which are, in our opinion, *the finest to be
found in the known universe*. In fact, we like them so much that Robert hacked into their mainframe
and made sure they built a Cracker Barrel in Wilmington.

**The Pernicious Puzzle**

On each table in the Cracker Barrel is a peg puzzle, which consists of a triangular block of wood
containing 15 holes, 14 of which have golf tees (aka pegs) in them. The game consists of jumping pegs over
one another and removing the jumped-over

peg, in a similar manner to checkers. The object is to
end up with as few pegs as possible, hopefully one.

It's more difficult than it looks, and so, after Robert failed to do better than 2 pegs (which, though it qualifies him as “Purty Darn Smart”, is an insult to any self-respecting Mad Overlord!), he decided to write a simple computer program that would play every single possible game, and tell him the results.

As it happened, Robert was on a trip to an Anime convention when he decided to do this, wrote the program during the convention, and had dinner at the same Cracker Barrel on the way back, wherein he proceeded to crush all comers.

Revenge, 'tis sweet.

#### More Than You Ever Wanted To Know About The Puzzle

While there are 15 possible starting positions for the pegs, to be a perfect player, you really only need to know how to play from 4 of them (pegs 1,2,4 and 5), because all the rest are either a reflection, rotation, or a reflection or rotation of the “core 4”.

For example, if the hole is at peg 11, you can rotate the puzzle to move peg 11 to peg 1, peg 3 is the mirror reflection of peg 2, and peg 14 can be made into peg 2 by a rotation and a reflection combined. By learning winning games from pegs 1,2,3,4 and 5 you can complete the puzzle without bothering with reflections at all.

There are a total of 1,945,839,290 possible games that can be played, of which only 438,984 of them are winning games with only 1 peg left.

The choice of the starting empty peg is very important. There are 29,760 possible winning games starting with pegs 1,11 or 15; 14,880 winners starting with pegs 2,3,7,10,12 or 14; and 85,258 when starting from pegs 4,6, or 13. But there are only 1550 solutions when starting from pegs 5,8, or 9!

Thus, when at dinner and challenged to play the game, always give the puzzle to your unsuspecting opponent with peg 5 empty, and watch him or her go down in flames. But when you take the puzzle, start with position 4 open, and even if you don't remember the moves, you're likely to do better (you're about 50 times more likely to luck out!)

Presented on this page are diagrams for sample winning games starting with any particular peg and, just for giggles, ending up whenever possible with the final peg on the starting hole. If you want to be a real ratfink, have someone try to do this with the empty peg starting at positions 5,8 or 9 – it's impossible! I've also included an example of the worst possible game! It turns out that it is possible to play a game that ends up with 10 pegs out of the original 14 on the board, but no legal moves!

#### Other Peg-Puzzle Obsessed Patrons

I am not the only person who has written about the nefarious peg-puzzle or written software to sneakily solve it. A search on google for cracker barrel peg puzzle will bring up some interesting pages (though, bwahahaha!, this one often comes up number one!). In particular you may like George Bell and Dan O'Brien's efforts. George in particular is to be commended for his deep analysis of the general peg-puzzle game as well as for documenting a set of simple playing rules that greatly increase your chances of winning.

#### Starting and Ending at Peg 1

**Start with peg 1 empty.**

**Move from peg 4 over
peg 2 to peg 1.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 4 over
peg 2 to peg 1.**

**List of Moves:**

Start with empty peg in hole 1

Move from 4 over 2 to 1

Move from 6 over 5 to 4

Move from 1 over 3 to 6

Move from 7 over 4 to 2

Move from 10 over 6 to 3

Move from 12 over 8 to 5

Move from 14 over 13 to 12

Move from 11 over 12 to 13

Move from 13 over 9 to 6

Move from 3 over 6 to 10

Move from 15 over 10 to 6

Move from 6 over 5 to 4

Move from 4 over 2 to 1

#### Starting and Ending at Peg 2

**Start with peg 2 empty.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**List of Moves:**

Start with empty peg in hole 2

Move from 7 over 4 to 2

Move from 6 over 5 to 4

Move from 1 over 3 to 6

Move from 2 over 4 to 7

Move from 10 over 6 to 3

Move from 12 over 8 to 5

Move from 14 over 13 to 12

Move from 11 over 12 to 13

Move from 13 over 9 to 6

Move from 3 over 6 to 10

Move from 15 over 10 to 6

Move from 6 over 5 to 4

Move from 7 over 4 to 2

#### Starting and Ending at Peg 3

**Start with peg 3 empty.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 13 over
peg 8 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 14 over
peg 9 to peg 5.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 10 over
peg 6 to peg 3.**

**List of Moves:**

Start with empty peg in hole 3

Move from 10 over 6 to 3

Move from 4 over 5 to 6

Move from 1 over 2 to 4

Move from 3 over 6 to 10

Move from 7 over 4 to 2

Move from 13 over 8 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

Move from 15 over 14 to 13

Move from 12 over 13 to 14

Move from 14 over 9 to 5

Move from 4 over 5 to 6

Move from 10 over 6 to 3

#### Starting and Ending at Peg 4

**Start with peg 4 empty.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 6 over
peg 3 to peg 1.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 13 over
peg 8 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 14 over
peg 9 to peg 5.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**List of Moves:**

Start with empty peg in hole 4

Move from 1 over 2 to 4

Move from 6 over 3 to 1

Move from 4 over 5 to 6

Move from 10 over 6 to 3

Move from 1 over 3 to 6

Move from 13 over 8 to 4

Move from 7 over 4 to 2

Move from 15 over 14 to 13

Move from 12 over 13 to 14

Move from 14 over 9 to 5

Move from 6 over 5 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

#### Starting at Peg 5 (no solutions end there!)

**Start with peg 5 empty.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 10 over
peg 9 to peg 8.**

**Move from peg 2 over
peg 5 to peg 9.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 9 to peg 13.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**List of Moves:**

Start with empty peg in hole 5

Move from 12 over 8 to 5

Move from 10 over 9 to 8

Move from 2 over 5 to 9

Move from 3 over 6 to 10

Move from 7 over 4 to 2

Move from 1 over 2 to 4

Move from 14 over 13 to 12

Move from 4 over 8 to 13

Move from 12 over 13 to 14

Move from 15 over 10 to 6

Move from 6 over 9 to 13

Move from 14 over 13 to 12

Move from 11 over 12 to 13

#### Starting and Ending at Peg 6

**Start with peg 6 empty.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 4 over
peg 2 to peg 1.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 15 over
peg 10 to peg 6.**

**List of Moves:**

Start with empty peg in hole 6

Move from 1 over 3 to 6

Move from 4 over 2 to 1

Move from 6 over 5 to 4

Move from 7 over 4 to 2

Move from 1 over 2 to 4

Move from 12 over 8 to 5

Move from 4 over 5 to 6

Move from 10 over 6 to 3

Move from 14 over 13 to 12

Move from 11 over 12 to 13

Move from 13 over 9 to 6

Move from 3 over 6 to 10

Move from 15 over 10 to 6

#### Starting and Ending at Peg 7

**Start with peg 7 empty.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**List of Moves:**

Start with empty peg in hole 7

Move from 2 over 4 to 7

Move from 6 over 5 to 4

Move from 1 over 3 to 6

Move from 7 over 4 to 2

Move from 10 over 6 to 3

Move from 12 over 8 to 5

Move from 14 over 13 to 12

Move from 11 over 12 to 13

Move from 13 over 9 to 6

Move from 3 over 6 to 10

Move from 15 over 10 to 6

Move from 6 over 5 to 4

Move from 2 over 4 to 7

#### Starting at Peg 8 (no solutions end there!)

**Start with peg 8 empty.**

**Move from peg 3 over
peg 5 to peg 8.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 7 over
peg 8 to peg 9.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 14 over
peg 9 to peg 5.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 1 over
peg 3 to peg 6.**

**List of Moves:**

Start with empty peg in hole 8

Move from 3 over 5 to 8

Move from 10 over 6 to 3

Move from 13 over 9 to 6

Move from 3 over 6 to 10

Move from 7 over 8 to 9

Move from 2 over 4 to 7

Move from 11 over 7 to 4

Move from 15 over 14 to 13

Move from 12 over 13 to 14

Move from 14 over 9 to 5

Move from 4 over 5 to 6

Move from 10 over 6 to 3

Move from 1 over 3 to 6

#### Starting at Peg 9 (no solutions end there!)

**Start with peg 9 empty.**

**Move from peg 2 over
peg 5 to peg 9.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 3 over
peg 5 to peg 8.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 6 over
peg 9 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 13 over
peg 8 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**List of Moves:**

Start with empty peg in hole 9

Move from 2 over 5 to 9

Move from 7 over 4 to 2

Move from 12 over 8 to 5

Move from 3 over 5 to 8

Move from 10 over 6 to 3

Move from 1 over 3 to 6

Move from 14 over 13 to 12

Move from 6 over 9 to 13

Move from 12 over 13 to 14

Move from 15 over 14 to 13

Move from 13 over 8 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

#### Starting and Ending at Peg 10

**Start with peg 10 empty.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 13 over
peg 8 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 14 over
peg 9 to peg 5.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**List of Moves:**

Start with empty peg in hole 10

Move from 3 over 6 to 10

Move from 4 over 5 to 6

Move from 1 over 2 to 4

Move from 7 over 4 to 2

Move from 10 over 6 to 3

Move from 13 over 8 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

Move from 15 over 14 to 13

Move from 12 over 13 to 14

Move from 14 over 9 to 5

Move from 4 over 5 to 6

Move from 3 over 6 to 10

#### Starting and Ending at Peg 11

**Start with peg 11 empty.**

**Move from peg 4 over
peg 7 to peg 11.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 1 over
peg 3 to peg 6.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 9 to peg 13.**

**Move from peg 13 over
peg 12 to peg 11.**

**List of Moves:**

Start with empty peg in hole 11

Move from 4 over 7 to 11

Move from 6 over 5 to 4

Move from 1 over 3 to 6

Move from 2 over 4 to 7

Move from 10 over 6 to 3

Move from 11 over 7 to 4

Move from 12 over 8 to 5

Move from 4 over 5 to 6

Move from 3 over 6 to 10

Move from 14 over 13 to 12

Move from 15 over 10 to 6

Move from 6 over 9 to 13

Move from 13 over 12 to 11

#### Starting and Ending at Peg 12

**Start with peg 12 empty.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 10 over
peg 9 to peg 8.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 14 over
peg 13 to peg 12.**

**List of Moves:**

Start with empty peg in hole 12

Move from 14 over 13 to 12

Move from 4 over 8 to 13

Move from 1 over 2 to 4

Move from 7 over 4 to 2

Move from 6 over 5 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

Move from 12 over 13 to 14

Move from 15 over 10 to 6

Move from 3 over 6 to 10

Move from 10 over 9 to 8

Move from 4 over 8 to 13

Move from 14 over 13 to 12

#### Starting and Ending at Peg 13

**Start with peg 13 empty.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 3 over
peg 5 to peg 8.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 10 over
peg 6 to peg 3.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 13 over
peg 9 to peg 6.**

**Move from peg 2 over
peg 5 to peg 9.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 6 over
peg 9 to peg 13.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 11 over
peg 12 to peg 13.**

**List of Moves:**

Start with empty peg in hole 13

Move from 4 over 8 to 13

Move from 1 over 2 to 4

Move from 3 over 5 to 8

Move from 7 over 4 to 2

Move from 10 over 6 to 3

Move from 12 over 8 to 5

Move from 13 over 9 to 6

Move from 2 over 5 to 9

Move from 3 over 6 to 10

Move from 15 over 10 to 6

Move from 6 over 9 to 13

Move from 14 over 13 to 12

Move from 11 over 12 to 13

#### Starting and Ending at Peg 14

**Start with peg 14 empty.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 6 over
peg 5 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 14 over
peg 13 to peg 12.**

**Move from peg 15 over
peg 10 to peg 6.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 10 over
peg 9 to peg 8.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**List of Moves:**

Start with empty peg in hole 14

Move from 12 over 13 to 14

Move from 4 over 8 to 13

Move from 1 over 2 to 4

Move from 7 over 4 to 2

Move from 6 over 5 to 4

Move from 2 over 4 to 7

Move from 11 over 7 to 4

Move from 14 over 13 to 12

Move from 15 over 10 to 6

Move from 3 over 6 to 10

Move from 10 over 9 to 8

Move from 4 over 8 to 13

Move from 12 over 13 to 14

#### Starting and Ending at Peg 15

**Start with peg 15 empty.**

**Move from peg 6 over
peg 10 to peg 15.**

**Move from peg 4 over
peg 5 to peg 6.**

**Move from peg 1 over
peg 2 to peg 4.**

**Move from peg 3 over
peg 6 to peg 10.**

**Move from peg 7 over
peg 4 to peg 2.**

**Move from peg 13 over
peg 8 to peg 4.**

**Move from peg 2 over
peg 4 to peg 7.**

**Move from peg 10 over
peg 9 to peg 8.**

**Move from peg 11 over
peg 7 to peg 4.**

**Move from peg 15 over
peg 14 to peg 13.**

**Move from peg 12 over
peg 13 to peg 14.**

**Move from peg 4 over
peg 8 to peg 13.**

**Move from peg 13 over
peg 14 to peg 15.**

**List of Moves:**

Start with empty peg in hole 15

Move from 6 over 10 to 15

Move from 4 over 5 to 6

Move from 1 over 2 to 4

Move from 3 over 6 to 10

Move from 7 over 4 to 2

Move from 13 over 8 to 4

Move from 2 over 4 to 7

Move from 10 over 9 to 8

Move from 11 over 7 to 4

Move from 15 over 14 to 13

Move from 12 over 13 to 14

Move from 4 over 8 to 13

Move from 13 over 14 to 15

#### The Worst Possible Game!

**Start with peg 5 empty.**

**Move from peg 12 over
peg 8 to peg 5.**

**Move from peg 3 over
peg 5 to peg 8.**

**Move from peg 14 over
peg 9 to peg 5.**

**Move from peg 8 over
peg 5 to peg 3.**

**List of Moves:**

Start with empty peg in hole 5

Move from 12 over 8 to 5

Move from 3 over 5 to 8

Move from 14 over 9 to 5

Move from 8 over 5 to 3