TECHNIQUE 1 OF 4

Legal jumps: check source, middle and landing hole

Read a jump as three consecutive holes on one row or column. All three conditions matter: occupied source, occupied middle and empty destination.

The rule and its limit

A classic jump travels exactly two grid positions horizontally or vertically. It moves the source peg to the destination and removes the middle peg. A gap in the middle, an occupied destination or a diagonal direction makes that proposed jump illegal.

A common mistake

A visually clear path is not enough. You cannot jump an empty hole, land on another peg, or cross two pegs in one classic jump.

PLAYABLE EXAMPLE 1

One legal jump to finish

Identify a legal orthogonal jump: occupied source, occupied middle, empty landing. Finish with one peg.

○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 1 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
R3C5 → R3C3	Remove the jumped peg at R3C4. 1 pegs remain.	Can finish with one peg in 0 further jumps.

Open this study’s full route and evidence →

PLAYABLE EXAMPLE 2

The middle peg matters

Identify a legal orthogonal jump: occupied source, occupied middle, empty landing. Finish with one peg.

○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 2 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
R5C1 → R5C3	Remove the jumped peg at R5C2. 2 pegs remain.	Can finish with one peg in 1 further jump.

Open this study’s full route and evidence →

A diagonal chain is still illegal

R1C1 and R2C2 hold pegs; R3C3 is empty. Consider only the proposed jump from R1C1 to R3C3.

The tempting move

Jump the peg at R1C1 over R2C2 into R3C3.

Why it fails

The three holes form a diagonal. This classic version allows only horizontal and vertical jumps.

What you can conclude

Reject that move regardless of the three occupancy values. Search for a side-aligned occupied, occupied, empty triple instead.

Try the idea in another position

R2C2 and R3C2 contain pegs, while R4C2 is empty. What changes if you jump from R2C2 to R4C2?

Check your reasoning

The jump is legal. R2C2 and R3C2 become empty, and R4C2 becomes occupied. All other holes retain their states.

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