PAPER DECISION STUDIES

Peg Solitaire — Decisions: compare what happens next

Four starting positions, then four separate answer sheets. The IDs match the online studies.

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.

Printing and using this pack

Use Print or Save as PDF. The first page contains instructions, the next four pages contain the tasks, and the remaining pages contain answers. An answer may continue onto another page. Check your print preview before choosing a page range. Print only the challenge pages if you want to keep answers separate.

Write a move and a reason before consulting the key. Rows count from the top and columns from the left. Four in a Row and Reversi diagrams state whose turn it is. The full online comparison includes all legal first moves; the answer sheets include the complete first-move comparison or a checked route.

Return to the online collection

CHALLENGE · peg-05

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

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

playfieldarcade.com/practice/peg/peg-05/ · Personal, family and classroom printing permitted.

CHALLENGE · 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

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

playfieldarcade.com/practice/peg/peg-06/ · Personal, family and classroom printing permitted.

CHALLENGE · peg-07

Read a finish backwards

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

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

playfieldarcade.com/practice/peg/peg-07/ · Personal, family and classroom printing permitted.

CHALLENGE · 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

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

playfieldarcade.com/practice/peg/peg-08/ · Personal, family and classroom printing permitted.

ANSWER · peg-05

A legal jump can lose the finish

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.

Every legal first jump

First move	Immediate effect	Checked consequence
R4C5 → R4C3	Remove the jumped peg at R4C4. 5 pegs remain.	No one-peg finish exists after this jump; every remaining legal branch was checked.
R5C1 → R5C3	Remove the jumped peg at R5C2. 5 pegs remain.	Can finish with one peg in 4 further jumps.
R5C5 → R3C5	Remove the jumped peg at R4C5. 5 pegs remain.	Can finish with one peg in 4 further jumps.

Checked route

Jump R5C1 → R5C3 over R5C2.
Jump R5C5 → R3C5 over R4C5.
Jump R2C5 → R4C5 over R3C5.
Jump R4C5 → R4C3 over R4C4.
Jump R5C3 → R3C3 over R4C3.

○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

Full starting diagram and all comparisons: playfieldarcade.com/practice/peg/peg-05/

ANSWER · peg-06

Choose between two futures

Every legal first jump

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.

Checked route

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.

○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

Full starting diagram and all comparisons: playfieldarcade.com/practice/peg/peg-06/

ANSWER · peg-07

Read a finish backwards

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. Read the final jump backward: the finish has its only peg at R3C3. Remove that peg and restore pegs at R5C3 and R4C3. 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.

Checked route

Jump R4C3 → R4C1 over R4C2.
Jump R2C2 → R4C2 over R3C2.
Jump R4C1 → R4C3 over R4C2.
Jump R5C4 → R5C2 over R5C3.
Jump R5C1 → R5C3 over R5C2.
Jump R5C3 → R3C3 over R4C3.

○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

Full starting diagram and all comparisons: playfieldarcade.com/practice/peg/peg-07/

ANSWER · peg-08

Build and unwind a longer chain

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.

Checked route

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.

○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

Full starting diagram and all comparisons: playfieldarcade.com/practice/peg/peg-08/