DECISION STUDY · peg-06

Choose between two futures

Compare all legal first jumps. Which preserve a one-peg finish, and which strand the position? Then play a successful branch.

○R1C1●R1C2●R1C3○R1C4○R1C5●R2C1○R2C2○R2C3○R2C4○R2C5○R3C1○R3C2○R3C3○R3C4○R3C5●R4C1○R4C2○R4C3●R4C4●R4C5○R5C1●R5C2○R5C3○R5C4○R5C5

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Select a peg, then one of its available empty landing squares. A jump removes the peg in between.

Keyboard: Tab to an enabled control, then press Enter or Space. The study starts from the diagram shown; reload can restore your own saved moves.

Try the task before inspecting the answer.

Worked moves are available when your board matches a checkpoint in the written route. If you choose another branch, inspect it, undo, or reset.

Show the starting-position answer and evidence

Every jump removes exactly one peg, so a one-peg finish needs 6 jumps. Every legal first jump is evaluated. A successful continuation is verified by a complete finishing route; a no-finish conclusion exhausts all remaining legal branches. The route below is one verified finish; its last peg may be anywhere on this classic board.

First move	Immediate effect	Checked consequence
R1C2 → R1C4	Remove the jumped peg at R1C3. 6 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R1C3 → R1C1	Remove the jumped peg at R1C2. 6 pegs remain.	Can finish with one peg in 5 further jumps.
R4C5 → R4C3	Remove the jumped peg at R4C4. 6 pegs remain.	Can finish with one peg in 5 further jumps.

One complete checked route

These moves start from the original diagram, not from any different choices you made above. Read coordinates at the moment each move is made.

Jump R1C3 → R1C1 over R1C2.
Jump R1C1 → R3C1 over R2C1.
Jump R3C1 → R5C1 over R4C1.
Jump R4C5 → R4C3 over R4C4.
Jump R5C1 → R5C3 over R5C2.
Jump R5C3 → R3C3 over R4C3.

After the first move

●R1C1○R1C2○R1C3○R1C4○R1C5●R2C1○R2C2○R2C3○R2C4○R2C5○R3C1○R3C2○R3C3○R3C4○R3C5●R4C1○R4C2○R4C3●R4C4●R4C5○R5C1●R5C2○R5C3○R5C4○R5C5

Verified finish

○R1C1○R1C2○R1C3○R1C4○R1C5○R2C1○R2C2○R2C3○R2C4○R2C5○R3C1○R3C2●R3C3○R3C4○R3C5○R4C1○R4C2○R4C3○R4C4○R4C5○R5C1○R5C2○R5C3○R5C4○R5C5

How this position was checked

Built by reversing legal jumps from one centre peg; the recorded forward construction is verified.

Explain what you learned

Choose one first move from the comparison table. Explain its effect without rereading the answer. Then change the first move and identify which part of the explanation changes. A checked route answers this starting position; it does not automatically apply to a new one.

Rules and limits

Playfield's classic version uses a full five-by-five grid of holes, not the traditional cross-shaped board. Jump one peg horizontally or vertically over exactly one adjacent peg into the empty hole immediately beyond. The jumped peg is removed. Finish with exactly one peg anywhere on the board; the classic version does not require a centre finish. Diagonal jumps and jumps over longer runs are not allowed.

Every classic jump removes exactly one peg, so a successful finish from N pegs uses N minus 1 jumps. That arithmetic does not prove a successful sequence exists. An available continuation is not proof of eventual solvability. Exact winning or losing claims require a complete checked sequence or exhaustive search of the stated position. The live generator uses reverse jumps to build reachable layouts, but a poor forward choice can still strand the pegs.

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Playfield Arcade · Updated 3 October 2026 · AI-assisted writing and code; examples checked against the local game rules. Our method · Report a correction