Clear the board in packages

Plan three jumps that clear a group of pegs and bring the first peg home, and see why an isolated peg cannot jump immediately.

Plan three jumps together

A package of three, and the peg that starts and ends the package.

Each jump takes one peg off, so it is easy to play one jump at a time and end up with pegs scattered all over the board. Scattered pegs are the problem: a peg with no peg beside it cannot jump and cannot be jumped, so it just sits there.

More

One useful pattern clears a package. With the bottom-left hole empty as shown, three pegs in a line and a fourth peg beside one end allow three jumps: the fourth peg jumps out over the package, one package peg jumps across, and the fourth peg jumps back into its starting hole. Nothing outside the package moves. Plan all three jumps; each destination must be empty when that jump happens.

So look for a line of three pegs with a fourth peg beside one end of it, and keep your pegs in one group as the board empties. On the cross, leave a package near the middle for last, because the middle hole is where the classic finish ends.

Lesson help

Clear a package of three at a time and keep the pegs in one group, so no peg is left with nothing beside it.

About this lesson

Try the method in a practice when you are ready.

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Plan three jumps together

Each jump takes one peg off, so it is easy to play one jump at a time and end up with pegs scattered all over the board. Scattered pegs are the problem: a peg with no peg beside it cannot jump and cannot be jumped, so it just sits there.

One useful pattern clears a package. With the bottom-left hole empty as shown, three pegs in a line and a fourth peg beside one end allow three jumps: the fourth peg jumps out over the package, one package peg jumps across, and the fourth peg jumps back into its starting hole. Nothing outside the package moves. Plan all three jumps; each destination must be empty when that jump happens.

So look for a line of three pegs with a fourth peg beside one end of it, and keep your pegs in one group as the board empties. On the cross, leave a package near the middle for last, because the middle hole is where the classic finish ends.

A package of three, and the peg that starts and ends the package.

Three jumps, and the first peg comes home

The peg in the top left corner jumps down over the peg below it and lands in the bottom left hole. One peg gone.

Now the peg on the right of the middle row jumps left over the middle one. Two pegs gone.

Last, the peg in the bottom left jumps back up over the peg that just landed beside it, and lands in the hole it started in. Three pegs gone, and the board is exactly as it was apart from the package.

After the first jump.
After the second jump.
One peg left, back where it began.

A peg on its own

Here are two pegs together in one corner and one peg on its own in the other.

The peg on its own has no peg beside it, in any direction.

One peg with nothing beside it.

Try it

What can the peg on its own do next?

  1. Nothing, until another peg lands beside it
  2. Jump to the empty hole two along
Show the answer

Nothing, until another peg lands beside it

Correct. A jump has to go over a peg, so a peg with nothing beside it cannot move, and nothing can jump over it either. It is not lost for good, because a peg can still land beside it later. That is why you keep the pegs in one group.

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