Peg Solitaire · Square

The square board has 36 holes in a 6×6 grid. Empty c3 and return to c3 in 34 jumps. It has four middle holes and no unique centre; diagonal jumps are not allowed.

The square, a board with no centre

Six holes by six holes, thirty-six in all, and nothing to be the middle of it. A square with an even side has four holes in its middle, so there is no single centre hole to empty.

We start at c3, off to one side of the middle, and finish back at c3. No diagonal jumps, no tricks: thirty-four straight jumps, across or up and down.

It is the plainest board here, and plain is a different kind of hard.

Square board at the start: 35 marbles and one empty hole, c3; the target ring is on c3; arrows show the first jumps, c1 over c2, a3 over b3, e3 over d3 or c5 over c4. — Every game starts like this: 36 holes, c3 empty. The first jump is c1 over c2, a3 over b3, e3 over d3 or c5 over c4, and after 34 jumps the last marble has to be back on c3.

How to play the square board

The board is a 6 by 6 grid, columns a to f and rows 1 to 6. The empty hole starts at c3. Four first jumps are possible, all landing on c3: from c1, a3, e3 or c5. Diagonal jumps are not allowed.

Each jump needs two neighbouring marbles in a straight line and an empty hole immediately beyond them. The jumped marble is removed; every jump reduces the count by one.
On square grids, jump horizontally or vertically. On the triangle, use any of the six directions parallel to its three sides. A diagonal on a square grid is never legal.
The marked hole is the required finish. One marble somewhere else is a different result, not a win in this target puzzle. You can undo a jump and explore a different route.
Our counter records individual jumps. Mathematical books sometimes group several jumps by the same marble into one “move”; those totals are not comparable.

Click or tap a marble. If only one jump is possible it happens at once; if there are several, outlined holes show where the marble can land and you pick one. You can also drag a marble onto a hole, or use the keyboard: arrow keys to move, Enter or Space to select and jump, Escape to clear, Ctrl or Cmd with Z to undo.

How to win the square

Thirty-five marbles means 34 jumps. The target ring is on c3. The win is the last marble returning there.

Square board strategy

Know your last jump. Four jumps can land on c3: c1 over c2, a3 over b3, e3 over d3, or c5 over c4. The last two marbles must be one of those pairs.
Watch the corners. In a square the corners have the fewest neighbours, so a marble left in one is easily stranded.
A square has no single centre, so there is no obvious opening to copy from other boards. Plan from c3 outwards.

The square board solution

The Solutions page replays one verified route of 34 jumps from c3 back to c3.

Questions people ask

Are diagonal jumps allowed?

No. On every square-grid board a jump runs across or up and down only.

Is there a solver for the square board?

There is no box where you type a position in, but the game has a solver of its own. The Hint button shows a jump from a route the game has checked can still win. If the search proves the target can no longer be reached, the game says so, which tells you to undo; if it reaches its search limit, the answer is simply unknown. A hint is marked in your result and keeps that game out of your best time.