DECISION STUDY · peg-08

Build and unwind a longer chain

Imagine undoing the final jump: one peg splits into two with an empty landing left behind. Use that idea to explain a complete forward 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

Loading playable study…

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 7 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. Read the final jump backward: the finish has its only peg at R3C3. Remove that peg and restore pegs at R3C5 and R3C4. That is exactly the two-peg position before the last jump. Continue reversing the written route from bottom to top: each undo restores its source and middle, and empties its landing. These reverse operations explain construction; the playable board permits only forward jumps.

First move	Immediate effect	Checked consequence
R2C2 → R4C2	Remove the jumped peg at R3C2. 7 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R2C3 → R4C3	Remove the jumped peg at R3C3. 7 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R2C3 → R2C1	Remove the jumped peg at R2C2. 7 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R2C5 → R4C5	Remove the jumped peg at R3C5. 7 pegs remain.	Can finish with one peg in 6 further jumps.
R3C2 → R1C2	Remove the jumped peg at R2C2. 7 pegs remain.	Can finish with one peg in 6 further jumps.
R3C2 → R3C4	Remove the jumped peg at R3C3. 7 pegs remain.	Can finish with one peg in 6 further jumps.
R3C3 → R1C3	Remove the jumped peg at R2C3. 7 pegs remain.	Can finish with one peg in 6 further jumps.
R3C3 → R3C1	Remove the jumped peg at R3C2. 7 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R3C5 → R1C5	Remove the jumped peg at R2C5. 7 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.

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 R2C5 → R4C5 over R3C5.
Jump R3C2 → R1C2 over R2C2.
Jump R2C4 → R2C2 over R2C3.
Jump R1C2 → R3C2 over R2C2.
Jump R3C2 → R3C4 over R3C3.
Jump R5C5 → R3C5 over R4C5.
Jump R3C5 → R3C3 over R3C4.

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