PAPER DECISION STUDIES

Four in a Row — Decisions: compare what happens next

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

Two players share a six-row, seven-column board. Orange starts, then Orange and Violet alternate dropping one token into a non-full column. It lands in the lowest empty square. Four or more consecutive tokens of one player horizontally, vertically or diagonally wins. A full board without a winner is a draw. This classic version has no token removal, wrapping or free placement above a gap. Row 1 is the top and row 6 the bottom.

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 · four-05

Remove the immediate danger

Orange to move. There is no immediate win for you. Which columns avoid handing the opponent a win on their next move?

·R1C1·R1C2·R1C3·R1C4·R1C5·R1C6·R1C7·R2C1·R2C2·R2C3·R2C4·R2C5·R2C6·R2C7OR3C1·R3C2·R3C3·R3C4·R3C5·R3C6·R3C7OR4C1·R4C2VR4C3OR4C4·R4C5·R4C6·R4C7VR5C1OR5C2VR5C3VR5C4·R5C5·R5C6·R5C7OR6C1VR6C2VR6C3OR6C4VR6C5·R6C6OR6C7

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

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

CHALLENGE · four-06

Compare safe and unsafe drops

Orange to move. There is no immediate win for you. Which columns avoid handing the opponent a win on their next move?

·R1C1·R1C2·R1C3·R1C4·R1C5·R1C6·R1C7·R2C1·R2C2·R2C3·R2C4·R2C5·R2C6·R2C7·R3C1·R3C2·R3C3·R3C4·R3C5·R3C6·R3C7·R4C1·R4C2·R4C3·R4C4·R4C5·R4C6·R4C7·R5C1·R5C2·R5C3·R5C4·R5C5·R5C6·R5C7OR6C1VR6C2·R6C3VR6C4VR6C5OR6C6OR6C7

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

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

CHALLENGE · four-07

A reply cannot cover every threat

Violet to move. Find a move after which every legal opposing reply leaves you an immediate winning move.

·R1C1·R1C2·R1C3·R1C4·R1C5·R1C6·R1C7OR2C1·R2C2·R2C3·R2C4OR2C5·R2C6·R2C7OR3C1OR3C2·R3C3·R3C4VR3C5·R3C6·R3C7VR4C1VR4C2·R4C3·R4C4VR4C5·R4C6VR4C7OR5C1OR5C2·R5C3VR5C4OR5C5·R5C6VR5C7OR6C1VR6C2OR6C3VR6C4VR6C5OR6C6OR6C7

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

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

CHALLENGE · four-08

Prove the fork against each reply

Orange to move. Find a move after which every legal opposing reply leaves you an immediate winning move.

VR1C1·R1C2·R1C3·R1C4VR1C5·R1C6·R1C7OR2C1·R2C2·R2C3·R2C4OR2C5·R2C6·R2C7OR3C1OR3C2·R3C3·R3C4VR3C5·R3C6OR3C7VR4C1VR4C2·R4C3OR4C4VR4C5·R4C6VR4C7OR5C1OR5C2VR5C3VR5C4OR5C5·R5C6VR5C7OR6C1VR6C2OR6C3VR6C4VR6C5OR6C6OR6C7

My move or route: __________________________________________

My reason: ________________________________________________

________________________________________________________

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

ANSWER · four-05

Remove the immediate danger

Columns avoiding an immediate opposing win: 3. This certifies only the next reply; it does not prove that the game can be won or drawn.

Every legal first move

First move	Immediate effect	Checked consequence
Column 1	Lands at R2C1.	Opponent can win next in column 3.
Column 2	Lands at R4C2.	Opponent can win next in columns 2, 3.
Column 3	Lands at R3C3.	No opponent win in one move; no forced next-turn win established.
Column 4	Lands at R3C4.	Opponent can win next in column 3.
Column 5	Lands at R5C5.	Opponent can win next in column 3.
Column 6	Lands at R6C6.	Opponent can win next in column 3.
Column 7	Lands at R5C7.	Opponent can win next in column 3.

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

ANSWER · four-06

Compare safe and unsafe drops

Columns avoiding an immediate opposing win: 3. This certifies only the next reply; it does not prove that the game can be won or drawn.

Every legal first move

First move	Immediate effect	Checked consequence
Column 1	Lands at R5C1.	Opponent can win next in column 3.
Column 2	Lands at R5C2.	Opponent can win next in column 3.
Column 3	Lands at R6C3.	No opponent win in one move; no forced next-turn win established.
Column 4	Lands at R5C4.	Opponent can win next in column 3.
Column 5	Lands at R5C5.	Opponent can win next in column 3.
Column 6	Lands at R5C6.	Opponent can win next in column 3.
Column 7	Lands at R5C7.	Opponent can win next in column 3.

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

ANSWER · four-07

A reply cannot cover every threat

Forced next-turn winning columns: 4. For each qualifying move, every legal reply has been checked, including replies that might win immediately for the opponent. The reply table gives your winning response.

Every legal first move

First move	Immediate effect	Checked consequence
Column 1	Lands at R1C1.	No opponent win in one move; no forced next-turn win established.
Column 2	Lands at R2C2.	No opponent win in one move; no forced next-turn win established.
Column 3	Lands at R5C3.	No opponent win in one move; no forced next-turn win established.
Column 4	Lands at R4C4.	Forces a win on your next turn against every legal reply.
Column 5	Lands at R1C5.	No opponent win in one move; no forced next-turn win established.
Column 6	Lands at R5C6.	No opponent win in one move; no forced next-turn win established.
Column 7	Lands at R3C7.	No opponent win in one move; no forced next-turn win established.

After column 4: every opposing reply

Opponent drops in	Your immediate winning response
Column 1	Columns 3, 4
Column 2	Columns 3, 4
Column 3	Columns 3, 4
Column 4	Column 3
Column 5	Columns 3, 4
Column 6	Columns 3, 4, 6
Column 7	Columns 3, 4

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

ANSWER · four-08

Prove the fork against each reply

Forced next-turn winning columns: 3, 4. For each qualifying move, every legal reply has been checked, including replies that might win immediately for the opponent. The reply table gives your winning response.

Every legal first move

First move	Immediate effect	Checked consequence
Column 2	Lands at R2C2.	No opponent win in one move; no forced next-turn win established.
Column 3	Lands at R4C3.	Forces a win on your next turn against every legal reply.
Column 4	Lands at R3C4.	Forces a win on your next turn against every legal reply.
Column 6	Lands at R5C6.	No opponent win in one move; no forced next-turn win established.
Column 7	Lands at R2C7.	No opponent win in one move; no forced next-turn win established.

After column 3: every opposing reply

Opponent drops in	Your immediate winning response
Column 2	Columns 3, 4
Column 3	Column 4
Column 4	Column 3
Column 6	Columns 3, 4
Column 7	Columns 3, 4

After column 4: every opposing reply

Opponent drops in	Your immediate winning response
Column 2	Column 3
Column 3	Column 3
Column 4	Column 3
Column 6	Column 3
Column 7	Column 3

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