Trevor Ng
The golf tee puzzle is a classic brainteaser that challenges players to use strategy and logic. The puzzle typically involves a triangular board with holes drilled into it and golf tees as pegs. The objective is to jump pegs over each other, removing the jumped pegs, and ultimately leaving only one peg remaining at the end of the game. While there are mathematically 6,816 solutions to the puzzle, careful planning is required to avoid making two bad moves, which can render the puzzle unsolvable. This puzzle is a great DIY project and can be easily made at home with some scrap wood, a drill, and golf tees.
| Characteristics | Values |
|---|---|
| Puzzle type | Peg game |
| Rules | Jump each peg over another peg, but only if there is an open space. Each peg you jump over must be removed. |
| Winning condition | Only one peg is left at the end of the game. |
| Starting position | Fill 14 holes with a tee, leaving one open at the top point of the triangle. |
| Board shape | Equilateral or isosceles triangle |
| Number of solutions | 6,816 |
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What You'll Learn
Understand the puzzle's mathematical theory
The "golf tee puzzle" or "peg game" is a puzzle involving a set of golf tees arranged in a triangle. The puzzle involves jumping one tee over another into an empty space and removing the jumped tee. The goal is to have only one tee remaining.
There is an intricate mathematical theory behind the puzzle, which, while not necessary to win, can be helpful to understand. For example, mathematically, the puzzle can be made impossible with two bad moves, so it is important to plan moves carefully. If moves are made randomly, there is a 50% chance the puzzle will become unsolvable within two moves.
The puzzle can be solved using the Klein 4-group, a mathematical concept in group theory. By colouring the holes with the three non-trivial elements of the Klein 4-group, the product of tees is invariant. This means that no matter the sequence of moves, the last remaining tee cannot be in a bottom corner position.
There are 6,816 solutions to the puzzle, which are modifications of two main solution patterns. One common and easy method is to begin with position 1 empty, which is the top point of the triangle. From there, specific moves can be made to reach the solution.
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Plan moves carefully to avoid an unsolvable puzzle
The golf tee puzzle, also known as the peg game or triangle peg board game, can be easily messed up with two bad moves, resulting in an unsolvable puzzle. To avoid this, it is important to plan your moves carefully and avoid jumping into a corner or from the middle of the board, which will almost guarantee a dead end.
The puzzle involves jumping each peg over another with the goal of having only one peg left at the end of the game. Each peg jumped over must be removed. To increase your chances of winning, you should start with position 1 empty, which is the top point of the triangle. This is the most common and easiest method.
It is also helpful to make a diamond shape with the pegs, which can be repeated throughout the board. While there are 6,816 solutions to the puzzle, they are all modifications of these two main solution patterns.
Additionally, it is worth noting that all solutions for the first three moves are the same for all starting positions except for position 5, which is the same as positions 8 and 9. These positions have very few solutions, with only 1,550 solutions for starting with hole 5, and all of them finish with the last peg in position 13. By being mindful of these tips and carefully planning your moves, you can increase your chances of solving the golf tee puzzle and avoiding an unsolvable situation.
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Learn the two main solution patterns
The golf tee puzzle, also known as the Cracker Barrel peg game, is a triangle-shaped board game with 15 holes. The aim is to jump each peg over another with an empty space in between and remove the peg that has been jumped over. The player wins if only one peg is left at the end of the game.
There are 6,816 solutions to the puzzle, but all of these are modifications of two main solution patterns. The first three moves are the most important, as after this, the board will always have two pyramids. The trick is to get to the same pattern after the first three moves, which is known as the \"goal shape\". From there, the puzzle can be solved as if it were starting position 1.
The first solution pattern starts with position 1 empty. This is the most common and easiest way to play. The basic pattern can be repeated throughout the board, helping the player to win the game. The second solution pattern starts with one of the other positions empty (2, 3, 4, 7, 10, or 13). This creates a diamond pattern and results in solutions that show remarkable symmetry.
It is worth noting that there is no set of moves to get to the "magic" third position when starting with hole 5 empty. While there are 1,550 solutions to starting with hole 5, every single one of them finishes with the last peg standing in position 13.
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Start with position 1 empty
The golf tee puzzle, also known as the peg game, is a puzzle consisting of a small wooden triangle board with 15 holes and 14 pegs. The player is supposed to jump pegs, removing the peg that has been jumped over, until there is only one peg left.
To start, leave position 1 empty. This is the top point of the triangle. The first three moves are as follows:
- Move peg 4 to position 1.
- Move peg 6 to position 4.
- Move peg 1 to position 6.
This will leave you with an empty diamond shape at the top of the triangle.
Now, move peg 7 to position 2, peg 13 to position 4, and peg 2 to position 7. To clear the second and bottom rows, move peg 10 to position 8, peg 7 to position 9, peg 15 to position 13, and peg 12 to position 14.
Finally, move peg 6 to position 13, peg 14 to position 12, and peg 11 to position 13. You should now have one peg left standing in position 13, and you have solved the puzzle.
It is worth noting that there are 6,816 solutions to this puzzle; however, they are all modifications of two main solution patterns. Additionally, while there are 1,550 solutions to starting with position 5 empty, every single one of them finishes with the last peg in position 13.
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Only jump pegs with an open space after
The peg game is a challenging puzzle with a simple objective: to be left with only one peg at the end. It is also known as the Cracker Barrel Peg Game, as it has been a fixture at Cracker Barrel restaurants since 1960. The game is played on a triangular board with 15 holes, labelled from 1 to 15. The objective is to jump pegs over other pegs to an open space and remove the jumped peg. This process is repeated until only one peg remains.
There are a few strategies to keep in mind when playing the peg game. Firstly, it is important to plan your moves carefully. If you move randomly, there is a 50% chance that you will end up with an unsolvable puzzle within just two moves. It is also recommended to avoid jumping into a corner or jumping from the middle of the board, as this can lead to a dead end.
- Start with the pegs arranged so that position 1 is left open. This will form a triangle with spaces 1 to 6.
- Clear this section by moving peg 6 to 1, peg 4 to 6, and peg 1 to 4. This will leave you with an empty diamond shape.
- Now focus on the middle row. Move peg 7 to 2 and peg 10 to 3.
- Use peg 13 to jump three times: move peg 13 to 4, then to 1, and finally from 1 to 6.
- Clear the last row by moving peg 11 to 13, peg 14 to 12, and peg 6 to 13.
- Finally, move peg 10 to 13.
By following these steps, you should be able to solve the puzzle and end up with only one peg remaining.
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Frequently asked questions
The golf tee puzzle is a triangle peg board game. The aim is to jump each peg over another peg, removing the peg that has been jumped over. The player wins if only one peg is left at the end of the game.
To set up the golf tee puzzle, you will need scrap lumber (a 6x6 that is 3/4" thick) and a drill with a 3/16" bit. Cut the wood into an isosceles triangle and drill 15 holes 5/8" deep. Blow out the holes to remove any sawdust and fill 14 of the holes with a golf tee, leaving one open.
There are 6,816 solutions to the puzzle, but they are all modifications of two main solution patterns. It is important to plan your moves carefully as two bad moves can make the puzzle impossible to solve.
