Playfield Arcade

TECHNIQUE 3 OF 4

Look ahead: inspect the pegs left behind

A legal jump can remove the very peg needed for a later connection. Compare the resulting positions before choosing between available jumps.

The rule and its limit

After a candidate jump, look for the next occupied, occupied, empty triples. A nonterminal position with none is an immediate dead end. If some remain, continue checking before making a claim about eventual success. Isolation is a warning about future access, not a universal rule that every currently separated peg is already lost.

A common mistake

Clearing a convenient region first can strand its last peg. Conversely, seeing one further legal jump does not prove that the rest of the sequence will work.

PLAYABLE EXAMPLE 1

A legal jump can lose the finish

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

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.

Compare the starting moves

Every jump removes exactly one peg, so a one-peg finish needs 5 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 moveImmediate effectChecked consequence
R4C5 → R4C3Remove the jumped peg at R4C4. 5 pegs remain.No one-peg finish exists after this jump; every remaining legal branch was checked.
R5C1 → R5C3Remove the jumped peg at R5C2. 5 pegs remain.Can finish with one peg in 4 further jumps.
R5C5 → R3C5Remove the jumped peg at R4C5. 5 pegs remain.Can finish with one peg in 4 further jumps.

Open this study’s full route and evidence →

PLAYABLE EXAMPLE 2

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

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.

Compare the starting moves

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 moveImmediate effectChecked consequence
R1C2 → R1C4Remove the jumped peg at R1C3. 6 pegs remain.No one-peg finish exists after this jump; every remaining legal branch was checked.
R1C3 → R1C1Remove the jumped peg at R1C2. 6 pegs remain.Can finish with one peg in 5 further jumps.
R4C5 → R4C3Remove the jumped peg at R4C4. 6 pegs remain.Can finish with one peg in 5 further jumps.

Open this study’s full route and evidence →

One legal opening strands three pegs

Only R1C1, R1C2, R1C4 and R2C2 contain pegs; every other hole is empty.

The tempting move

Jump R1C2 over R2C2 into R3C2 because the downward jump is legal.

Why it fails

That leaves pegs at R1C1, R1C4 and R3C2, with no adjacent pair available for another jump. The attempt stops with three pegs.

What you can conclude

A checked alternative is R1C1 to R1C3, then R1C4 to R1C2, then R1C2 to R3C2. Each jump removes its middle peg and the sequence ends with one. The choice of opening jump matters.

Try the idea in another position

Only R3C1, R3C2 and R3C4 contain pegs on a five-by-five board. What two-jump sequence finishes with one peg?

Check your reasoning

Jump R3C1 over R3C2 to R3C3. The remaining pegs are R3C3 and R3C4. Then jump R3C3 over R3C4 to R3C5. One peg remains at R3C5, so this is a complete checked finish.

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