Peg game solver facts at a glance
The peg game solver plays out every possible jump on the 15-hole triangle board, so it always knows whether one peg is still possible from where you are. It is free, needs no account and runs in your browser.
| Board | 15 holes in 5 rows, numbered 1 at the top to 15 at the bottom right |
|---|---|
| Start | 14 pegs and any one empty hole; or set up any board you are stuck on |
| Perfect game | 13 jumps, one peg left; possible from every one of the 15 starting holes |
| Ways to win, top hole empty | 29,760 different jump sequences end with one peg |
| Ways to win, hole 5 empty | 1,550, the fewest of any start |
| Worst finish | With the top hole empty, a game can get stuck with as many as 8 pegs left |
| Hint | The next jump that still leads to the fewest pegs possible from your board |
| Price and setup | Free, no account, no download; runs in your browser |
How to use the peg game solver
Play on the board above, and ask for help only when you want it: a hint shows one jump, the solution shows all of them.
- Pick the empty hole. The board starts with the top hole empty. To start from another hole, press Choose the empty hole and tap the peg to take out.
- Jump. Tap a peg, then tap the empty hole two steps away in a straight line. The peg in between is removed.
- Ask for a hint. Hint marks the next jump that keeps a one-peg finish possible, or the best finish left if one peg is no longer possible.
- See the whole solution. Show the solution lists every jump from your current board. Do the next jump plays them one at a time.
- Solve a real board. Press Set up my board, tap holes to add or remove pegs until it matches the board in front of you, then press Show the solution.
How to win the peg game every time
With the top hole empty, this sequence of 13 jumps leaves one peg. Hole numbers go 1 at the top, 2 and 3 in the second row, 4 to 6 in the third, 7 to 10 in the fourth and 11 to 15 along the bottom.
- 4 over 2 into 1
- 6 over 5 into 4
- 1 over 3 into 6
- 7 over 4 into 2
- 10 over 6 into 3
- 12 over 8 into 5
- 13 over 9 into 6
- 2 over 5 into 9
- 3 over 6 into 10
- 15 over 10 into 6
- 6 over 9 into 13
- 14 over 13 into 12
- 11 over 12 into 13
Two habits help on any start: keep pegs together instead of leaving lone pegs in the corners, since a peg in a corner can never be jumped over and can only leave by jumping out itself; and before each jump, check that the hole you empty can be filled again later.
The Cracker Barrel peg game and the scale on the board
This is the same puzzle as the wooden triangle with golf tees found on Cracker Barrel restaurant tables, also called the tricky triangle, the golf tee game or Hi-Q in some families. Those boards print a scale that rates you by the number of pegs left: one peg is the top rating, and four or more is the bottom. This page is not affiliated with Cracker Barrel; Cracker Barrel is a trademark of its owner.
Which start is easiest?
Every one of the 15 starting holes can be won with one peg, but some give far more ways to do it. With hole 4, 6 or 13 empty (the middle of each side), 85,258 jump sequences win. With a corner empty, 29,760 win. With hole 5, 8 or 9 empty (the three inside holes), only 1,550 win, and the last peg always lands in one particular hole: 13 when you start from 5. If you want the last peg to end in the hole you started from, start from a corner or the middle of a side; from the three inside holes that finish is impossible.
How the solver works
The board has only 15 holes, so there are at most 32,768 arrangements of pegs. The solver tries every jump from your board, then every jump after that, and remembers each arrangement it has already ruled out, so the whole search takes a fraction of a second. It finds the fewest pegs reachable from your board first, then a sequence of jumps that gets there.
Frequently asked questions
Can you always win the triangle peg game?
Yes, from any starting hole. With 14 pegs and one empty hole, 13 jumps can always leave one peg, though the number of ways to do it ranges from 1,550 to 85,258 depending on which hole starts empty.
What is the solution to the Cracker Barrel peg game?
With the top hole empty: 4 over 2 into 1, 6 over 5 into 4, 1 over 3 into 6, 7 over 4 into 2, 10 over 6 into 3, 12 over 8 into 5, 13 over 9 into 6, 2 over 5 into 9, 3 over 6 into 10, 15 over 10 into 6, 6 over 9 into 13, 14 over 13 into 12, 11 over 12 into 13. For any other start, play it on this page and press Show the solution.
How are the holes numbered?
Hole 1 is the top. The second row is 2 and 3, the third 4 to 6, the fourth 7 to 10, and the bottom row 11 to 15, each row from left to right. The board on this page shows the numbers.
Can I solve a board I am stuck on?
Yes. Press Set up my board, tap holes until the pegs match your board, and press Show the solution. If one peg is no longer possible, the solver says how few pegs you can still finish with and how.
Can the last peg end in the hole that started empty?
From a corner or from the middle of a side, yes. From the three inside holes, 5, 8 and 9, no: the last peg always ends somewhere else.
Is the peg game solver free?
Yes. It is free, with no account and no download, and it runs in your browser. A board link keeps the pegs in the link itself.