Peg board game solutions

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# Peg board game solutions

The hole triangle peg board game is a modern version of a game that has been played in Europe since the end of the 17th century. In the United States, Herbert M. Smith patented a triangular version of the game in It is also known as peg solitaire or the Cracker Barrel puzzle. The puzzle gained in popularity when the restaurant put one on every table to amuse patrons waiting for their food. The game consists of 14 pegs set in a triangle shape with 15 holes like bowling pins, but with one more row.

One of the spaces in the triangle is left empty, and the object is to jump pegs, removing each peg jumped, until you are left with only one. Place 14 pegs in the hole triangular board, leaving one hole empty.

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In your mind, number the holes from 1 to 15, going left to right, so that 1 is the tip of the triangle and 15 is the right-most hole in the bottom row. Remove the peg from hole 1, leaving the tip of the triangle empty. Jump pegs in the following order, removing each peg jumped: from 4 to 1, from 6 to 4, from 1 to 6 and from 7 to 2.

You will be left with holes 1, 2, 3 and 5 empty in a diamond shape. Jump from 13 to 4, from 2 to 7, from 10 to 8, from 7 to 9, from 15 to 13, from 12 to 14, from 6 to 13, from 14 to 12 and from 11 to This solution will also work with starting points at holes 11 and 15 by rotating the board to place those holes at the top. Repeat Step 1. Remove the peg from hole 2.

Jump from 7 to 2, from 13 to 4 and from 11 to Rotate the board to the right so that hole 11 now becomes hole 1, and you will see the same diamond-shaped pattern of vacant holes.

Continue playing as in Step 2, from the fourth move. By mirroring the first three moves of Step 3, this solution will also work from a beginning empty position at holes 3, 7, 10, 12 and Remove the peg from hole 4. Jump from 13 to 4, from 10 to 8 and from 15 to Rotate the board to the left, so that hole 15 is now hole 1. Note the diamond shape of empty holes and continue from the fourth move in Step 2. With mirroring of the first three moves, this solution will also work for vacant positions at holes 6 and Start at the midpoint of an edge for another possible solution.

Remove the third peg from any one side, so that there are two pegs on either side of a vacant hole. Align the board so this vacant hole is on the bottom of the triangle, and is, specifically, hole Jump from 11 to 13, from 14 to 12, from 4 to 13, from 1 to 4, from 12 to 14, from 6 to 13, from 15 to 6, from 7 to 2, from 2 to 9, from 3 to 10, from 10 to 8, from 14 to 12 and from 12 to 5.

Add variety to the Step 2 solution by again leaving the tip of the triangle empty. Jump the pegs from 4 to 1, from 6 to 4, from 15 to 6, from 3 to 10, from 13 to 6, from 11 to 13, from 14 to 12, from 12 to 5, from 10 to 3, from 7 to 2, from 1 to 4, from 4 to 6 and from 6 to 1. You will be left with one peg in hole 1, which was vacant at the beginning of the game. Challenge yourself by beginning from the interior. Remove the peg at hole 5. Jump from 12 to 5, from 14 to 12, from 10 to 8, from 3 to 10, from 2 to 9, from 7 to 2, from 15 to 6, from 6 to 13, from 12 to 14, from 1 to 4, from 4 to 13, from 14 to 12 and from 11 to This solution works backward from the solution in Step 5.

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By: Kira Jaines Updated April 12, Share It.During these challenging times, we guarantee we will work tirelessly to support you. We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission — to help everyone in the world learn how to do anything — no matter what.

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Updated: June 27, References. Peg Solitaire Sailor's Solitaire is a very popular single player game played with a board having holes in the pattern of a plus sign. There are pegs in all the holes except one.

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To create this article, 9 people, some anonymous, worked to edit and improve it over time.Although peg solitaire is a challenging game with numerous variations that keep even seasoned puzzlers interested, the rules are simple enough for young children to learn how to play. Peg solitaire has been played for over years and is also known by other names, such as Hi-Q and marble solitaire.

Peg solitaire is traditionally played on a board with 33 small holes arranged in the shape of a plus sign, with three columns of seven holes intersecting with three rows of seven holes.

Also included with the game are 32 pegs that fit into the holes. Peg solitaire can be played on other boards with the same arrangement, such as a piece of paper with circles drawn on it for the holes and pennies as the pegs. Before beginning peg solitaire, the player should set up the board by placing one peg in each hole except for the center hole. Peg solitaire is played by jumping a peg over another other peg into an empty hole on the other side. Pegs cannot jump diagonally, nor can they jump over more than one peg at a time.

They can, however, chain together multiple jumps by hopping over one peg into an empty hole and then, either in the same direction or a different direction, hopping from that hole over one more peg into another empty hole. Multiple jumps like this can continue as long as possible, as in Checkers.

When a peg is hopped over, it is immediately removed from the game board. The goal of peg solitaire is to remove all the pegs from the board except one, which should end up in the center hole that was empty at the beginning of the game. InErnest Bergholt developed a winning solution that required only 18 moves, where a move was picking up a peg and legally jumping it over one or more pegs before setting it down.

For young children, a more appropriate goal may be to end with five or fewer pegs on the board. Peg solitaire has a number of alternate initial configurations of the pegs, including an arrow, pyramid, fireplace and diamond. In addition, peg solitaire can be played on alternate boards such as a board of 15 holes arranged in a triangle, where pegs can jump horizontally or diagonally.

By: Kristen May Updated April 12, Share It.During these challenging times, we guarantee we will work tirelessly to support you.

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We will continue to give you accurate and timely information throughout the crisis, and we will deliver on our mission — to help everyone in the world learn how to do anything — no matter what. Thank you to our community and to all of our readers who are working to aid others in this time of crisis, and to all of those who are making personal sacrifices for the good of their communities.

We will get through this together. Updated: March 29, Reader-Approved References. You may have come across the "Peg Game" in a number of restaurants throughout the country. The game consists of a small wooden triangle board with 15 holes in it and 14 pegs.

Starting with one empty spot, the player is supposed to jump pegs until there is only one left. Some of these games state that if you can complete them, you're a genius- so here's an easy strategy to win the game and impress your family and friends!

Each time you jump a peg, you remove it from the board. To set up the game, put 1 peg into each slot except for the slot at the top of the triangle. To win the peg game, start with the top slot empty. Jump peg 4 to position 1, peg 6 to position 4, and peg 1 to position 6, to create a diamond-shaped opening at the top of the board. Next, move peg 7 to position 2, peg 13 to position 4, and peg 10 to position 8. Then, move peg 2 to position 7, then again to position 9, and peg 15 to position To get your pegs in the last row, move peg 12 to position 14 and peg 6 to position Complete the last moves by jumping peg 14 to position 12 and peg 11 to position For more information, including the theory behind the game, scroll down!

Well now you can always solve the puzzzle if you remember this method. Did you use this instructable in your classroom? Add a Teacher Note to share how you incorporated it into your lesson.

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. Leaving one peg is easy. I'm looking for the solution to leaving one peg in all three corners.

Anyone know how? Reply 4 years ago. Sorry to be the one to have to tell you this, but your hope of finding a solution "leaving one peg in all three corners" is impossible. Great, right? All the pegs are in it, so do I just pull a peg and put it aside, so there will be a place to serve as a jumping area, or something else? I loved playing this game so much as a kid I decided to make a 75 level mobile game based on it. Reply 4 years ago on Introduction.

I only did it with one left once in my life before, but thanks to you, now I can memorize it! Also, see if you can leave 10 pegs instead of one.

I start with the middle peg of the bottom edge empty where you started the blue peg. If I have one odd-colored peg, I put it in the top corner. Then I can announce to the amazed onlookers that not only can I leave just one peg at the end, but it will be the odd colored one, and it will be in the hole that was empty to begin with. By Derpancakes Follow. More by the author:. Add Teacher Note.

## How to Solve a Triangle Peg Board Puzzle

Since it is hard to put into words what you should do, just follow the pictures below. If you have done everything right, you should only have one peg left. Good luck! Did you make this project? Share it with us! I Made It!

Solitaire game Solution

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Best regards, Grover. Cyncha 4 years ago. I find myself in possession of a brand new peg game. Ryan Shelby.

MonkiMan 6 years ago on Introduction.The classic peg game is found in Cracker Barrel restaurants and consist of a triangular board with 15 holes. You start with 14 pegs and one empty hole. You jump a peg over another peg into an empty hole. The peg that is jump over is removed from the board. This process continues until there is only one remaining peg or no more valid moves. Click the links below to see step-by-step instructions on how to solve the game. The solutions are categorized by the starting position.

There are four unique starting positions.

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All the other starting positions are just rotations or reflections of the board. The table below gives statistics for each starting position. Click the link in each row of the table to view step-by-step solutions and in depth analysis for each starting position. The see how to solutions were found and to download all the solutions as directed graphs view the programming guide. Peg Game Solutions. The Peg Game The classic peg game is found in Cracker Barrel restaurants and consist of a triangular board with 15 holes.

Solutions The solutions are categorized by the starting position. All Content Copyright All Rights Reserved.When visiting the Cracker Barrel restaurant, you will find a peg triangle board game on each table. This page describes how to solve the puzzle from any starting position. 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. 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! 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,and This shape is not too critical, the photo just shows the puzzle progressing. 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".

For the other starting positions except position 5 which we will cover laterthe same solution is used after the third jump.

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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.

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.

### The Peg Game

Even if seen backwards, after the first 3 moves, both line up for the same standard solution. 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. 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!