Here are my solutions.
if you number the pegs 0-9 and A-F you get:
0
1 2
3 4 5
6 7 8 9
A B C D E
Winning Games
take| games with | games ending | Possible | same as
out | one left | at start | games
--------------------------------------------------------------------------------
0 | 29760 (2.30%) | 6816 (0.52%) | 1293178 | A,E
1 | 14880 (2.21%) | 720 (0.10%) | 671084 | 2,6,9,B,D
3 | 85258 (3.28%) | 51452 (1.98%) | 2592132 | 5,C
4 | 1550 (0.47%) | 0 (0.00%) | 323872 | 7,8
--------------------------------------------------------------------------------
All | 438984 (2.63%) | 179124 (1.07%) | 16654050
Here are three solutions ending at start with 0,1,3 empty.
If you start with a middle one empty (4,7,8) there are no solutions with ending at start.
The solution is read as (peg to move, peg to jump, peg at end) for each move
***
[(3, 1, 0), (5, 4, 3), (0, 2, 5), (6, 3, 1), (9, 5, 2), (B, 7, 4), (D, C, B), (A, B, C), (C, 8, 5),
(2, 5, 9), (E, 9, 5), (5, 4, 3), (3, 1, 0)]
***
[(6, 3, 1), (5, 4, 3), (0, 2, 5), (1, 3, 6), (9, 5, 2), (B, 7, 4), (D, C, B), (A, B, C), (C, 8, 5),
(2, 5, 9), (E, 9, 5), (5, 4, 3), (6, 3, 1)]
***
[(0, 1, 3), (5, 2, 0), (3, 4, 5), (9, 5, 2), (0, 2, 5), (C, 7, 3), (6, 3, 1), (E, D, C), (B, C, D), (D, 8, 4), (5, 4, 3), (1, 3, 6), (A, 6, 3)]
When visiting the Cracker Barrel restaurant, you will find a 15-peg triangle board game on each table. This page describes how to solve the puzzle from any starting position.
The board has the form of a plus sign + 2 The goal is to jump a peg over another peg onto a hole. You can jump only horizontally or vertically. These are the rules: You must jump each peg over another peg, but only if there is an open space. Each peg you jump over must be removed. You win if only one peg is left at the end of the game. Now, my husband thrives on puzzles and games like this and he can figure things out quickly.
The game board is a triangle with 15 holes in the same shape as bowing pins, except with an extra row. The game starts with pegs (golf tees) in all the holes except one; the goal is to jump pegs one at a time, removing the jumped peg until only one peg remains. The instructions on the board say that if you leave only one peg, you are a genius. I suspect that the genius title is overstated, but if you follow the instructions on this page and you're sure to impress the family!
If you find this a useful page or if you have recommendations for changes, send an email to peggame at this domain.
Enjoy,
Joe Nord
For the pages that follow, the puzzle is viewed in this orientation and the hole numbers referenced. Photographs follow showing the board from start of game through completion.
The normal starting hole (empty hole) is hole #1. The initial discussion on this page shows how to solve the puzzle with hole #1 empty. That is followed by instructions on how to solve for the other starting positions, with the happy addition that most of the starting positions are just variations of the standard #1 start. After 3 moves, they all look the same; except the evil #5! Download lagu untuk game guitar hero 3.
The first 3 jumps are: 4-1, 6-4 and 1-6. With these complete, the 'magic' base follows. This shape will be referenced later in this document as the 'goal position' for the other variations of the game using different starting holes. Learning to solve the puzzle from this point is the key to success with the game.
The next moves, 7-2, 13-4 and 2-7. This shape is not too critical, the photo just shows the puzzle progressing.
The next steps are to clear the second from bottom row (the yellow tees) and the bottom row.
First, 10-8, 7-9 clears the second row.
15-13 and 12-14 clears the bottom. To mix it up, jump them in reverse and it won't look like you're solving the puzzle the same way every time.
Almost there, the diagonal jump clears all but the bottom of the puzzle and the bottom clears 'easy'.
6-13, 14-12 and 11-13 > Winner!
Starting position (1) - Full solution
4 | 1 |
6 | 4 |
1 | 6 |
7 | 2 |
13 | 4 |
2 | 7 |
10 | 8 |
7 | 9 |
15 | 13 |
12 | 14 |
6 | 13 |
14 | 12 |
11 | 13 |
For the other starting positions (except position 5 which we will cover later), the same solution is used after the third jump. The 'trick' is to get to the same pattern after the first three moves, the goal shape. From there, solve solve as if it were starting position 1. Notice that there is only one sequence to remember as you can get to the goal position from any of the starting positions based purely on shape.
Download adobe premiere pro cs4 32 bit portable. Here are the moves for 'after' the goal position is reached.
7 | 2 |
13 | 4 |
2 | 7 |
10 | 8 |
7 | 9 |
15 | 13 |
12 | 14 |
6 | 13 |
14 | 12 |
11 | 13 |
There are 15 pegs in the board, but only 4 starting positions. For example, all the points are position '1', even if they are otherwise called '11' or '15' the puzzle is the same once you rotate the board; even if only mentally. 2 and 3 are really the same if you view them 'mirrored'. Even if seen backwards, after the first 3 moves, both line up for the same standard solution. Starting positions 4/6 are also swappable; 13 is the same as 4/6 once you rotate the board.
Here are all the starting positions.
1 | 1, 11, 15 |
2 | 2, 3, 7, 12, 10, 14 |
4 | 4, 6, 13 |
5 | 5, 8, 9 |
The neat thing to observe is that start positions 1, 2 and 4 and 11, 15, 3, 7, 12, 10, 14, 6 and 13 are really the same as they have the same solution once you get past the first 3 moves! This means that there are only 2 puzzle solutions that need to be memorized to solve all positions on the puzzle. If someone figures out how to get to the 'magic' 3rd position when start with hole 5 empty, please let me know.
First three moves for starting position (1, 11, 15 -- Collectively called '1').
Starting hole | Move 1 | Move 2 | Move 3 | Comments |
1, 11, 15 | 4-1 | 6-4 | 1-6 | |
2, 3, 7, 12, 10, 14 | 7-2 | 13-4 | 11-13 | Rotate right |
4, 6, 13 | 13-4 | 10-8 | 15-13 | Rotate left |
I have not found a method to get to the 'same as the others' solution when start with hole #5 (aka 8, 9). A full solution follows and interestingly, it also ends with the final peg standing in hole 13; there must be a good reason. With practice, solving this 'hard one' is really just remembering that there are only 2 possible first moves and this solution starts from the right, the next couple moves are filling the pegs just jumped over or from and the 4th is opening the middle hole on the right side of the triangle. From there, it pretty much solves itself! ?
14 | 5 |
7 | 9 |
2 | 7 |
6 | 4 |
7 | 2 |
1 | 4 |
15 | 6 |
3 | 10 |
12 | 14 |
10 | 8 |
4 | 13 |
14 | 12 |
11 | 13 |