TRIANGLES

THE CRACKER BARREL TRIANGLE GAME

Anyone who has been to Cracker Barrel will recognize this game. My family stops at Cracker Barrel once a year on our annual trip down to Florida for spring break. My older brother and I have this ongoing competition to see who can get down to only one piece on the board. He's a super competitive engineering math guy, so he always tends to win. At everything. And in this case, it usually ends with me having to eat something gross. But the more I thought about this game, I started to wonder if there is some kind of pattern to go with finishing it down to one piece every time. I started to experiment with the game to see if I could find a pattern that would guarantee a win every time. Because I do not have one of these games in my possession, I found an online version to play around with. You can find that version here: http://www.memory-improvement-tips.com/pegs.html

The instructions for the game are as follows: 

After a lot of experimenting, I finally figured out a pattern that worked. This pattern starts with the top hole empty. (It can be any of the corners, just depends on which way you turn the triangle). When I reference the numbers, I am numbering the holes from top-down. Like this:

The first 3 jumps to the pattern are:  4-1, 6-4 and 1-6.

The next moves: 7-2, 13-4 and 2-7.

Next: 10-8 and 7-9 clear the second row

15-13 and 12-14 clears the bottom

Now for the last step: 6-13, 14-12 and 11-13. WINNER!

Note that this pattern is only made through an hour or so of trial and error. I played the game multiple times, each time recording my moves. Many times it ended in failure, with multiple pegs left on the board. This pattern was a success. It is proven to work every time that the game is started with the first hole left empty.