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Platon Sudoku · Sudoku Study

Avoidable Rectangle · Step-by-step example

An avoidable rectangle combines placed digits and candidates in four cells across exactly two boxes. Completing the alternating pair would create an interchangeable rectangle. Remove the candidate that would complete the deadly rectangle.

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

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Recognize the pattern

An avoidable rectangle combines placed digits and candidates in four cells across exactly two boxes. Completing the alternating pair would create an interchangeable rectangle.

How to find it

Find the placed and candidate corners, then test whether the target candidate would complete the alternating rectangle.

What it allows

Remove the candidate that would complete the deadly rectangle.

Avoid the mix-up

Unlike an ordinary unique rectangle, some corners are filled. Check the original givens and the exact two-box geometry.

Step-by-step example · Top left

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
Step 2 · Identify the three player-entered values

The values R2C6=4, R9C4=4, R9C6=5 were entered by the player during solving; none is a given clue. The remaining corner is R2C4=5. Only player-entered values may participate in this swap.

The values R2C6=4, R9C4=4, R9C6=5 were entered by the player during solving; none is a given clue. The remaining corner is R2C4=5. Only player-entered values may participate in this swap.
The values R2C6=4, R9C4=4, R9C6=5 were entered by the player during solving; none is a given clue. The remaining corner is R2C4=5. Only player-entered values may participate in this swap.
Step 3 · Compare the two rectangle fillings

Completing the corner with R2C4=5 gives R2C6=4, R9C4=4, R9C6=5, R2C4=5. Swapping the rectangle digits gives R2C6=5, R9C4=5, R9C6=4, R2C4=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.

Completing the corner with R2C4=5 gives R2C6=4, R9C4=4, R9C6=5, R2C4=5. Swapping the rectangle digits gives R2C6=5, R9C4=5, R9C6=4, R2C4=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Completing the corner with R2C4=5 gives R2C6=4, R9C4=4, R9C6=5, R2C4=5. Swapping the rectangle digits gives R2C6=5, R9C4=5, R9C6=4, R2C4=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Step 4 · Do not complete the swappable rectangle

Placing R2C4=5 would complete a swappable rectangle with the three player-entered values. Remove R2C4=5; the player entries themselves remain unchanged.

Placing R2C4=5 would complete a swappable rectangle with the three player-entered values. Remove R2C4=5; the player entries themselves remain unchanged.
Placing R2C4=5 would complete a swappable rectangle with the three player-entered values. Remove R2C4=5; the player entries themselves remain unchanged.

What it allows

Placing R2C4=5 would complete a swappable rectangle with the three player-entered values. Remove R2C4=5; the player entries themselves remain unchanged.

Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.
Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.

Step-by-step example · Top right

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
Step 2 · Identify the three player-entered values

The values R3C2=5, R6C2=2, R6C3=5 were entered by the player during solving; none is a given clue. The remaining corner is R3C3=2. Only player-entered values may participate in this swap.

The values R3C2=5, R6C2=2, R6C3=5 were entered by the player during solving; none is a given clue. The remaining corner is R3C3=2. Only player-entered values may participate in this swap.
The values R3C2=5, R6C2=2, R6C3=5 were entered by the player during solving; none is a given clue. The remaining corner is R3C3=2. Only player-entered values may participate in this swap.
Step 3 · Compare the two rectangle fillings

Completing the corner with R3C3=2 gives R3C2=5, R6C2=2, R6C3=5, R3C3=2. Swapping the rectangle digits gives R3C2=2, R6C2=5, R6C3=2, R3C3=5. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.

Completing the corner with R3C3=2 gives R3C2=5, R6C2=2, R6C3=5, R3C3=2. Swapping the rectangle digits gives R3C2=2, R6C2=5, R6C3=2, R3C3=5. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Completing the corner with R3C3=2 gives R3C2=5, R6C2=2, R6C3=5, R3C3=2. Swapping the rectangle digits gives R3C2=2, R6C2=5, R6C3=2, R3C3=5. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Step 4 · Do not complete the swappable rectangle

Placing R3C3=2 would complete a swappable rectangle with the three player-entered values. Remove R3C3=2; the player entries themselves remain unchanged.

Placing R3C3=2 would complete a swappable rectangle with the three player-entered values. Remove R3C3=2; the player entries themselves remain unchanged.
Placing R3C3=2 would complete a swappable rectangle with the three player-entered values. Remove R3C3=2; the player entries themselves remain unchanged.

What it allows

Placing R3C3=2 would complete a swappable rectangle with the three player-entered values. Remove R3C3=2; the player entries themselves remain unchanged.

Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.
Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.

Step-by-step example · Bottom left

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
Step 2 · Identify the three player-entered values

The values R1C1=6, R1C2=1, R4C2=6 were entered by the player during solving; none is a given clue. The remaining corner is R4C1=1. Only player-entered values may participate in this swap.

The values R1C1=6, R1C2=1, R4C2=6 were entered by the player during solving; none is a given clue. The remaining corner is R4C1=1. Only player-entered values may participate in this swap.
The values R1C1=6, R1C2=1, R4C2=6 were entered by the player during solving; none is a given clue. The remaining corner is R4C1=1. Only player-entered values may participate in this swap.
Step 3 · Compare the two rectangle fillings

Completing the corner with R4C1=1 gives R1C1=6, R1C2=1, R4C2=6, R4C1=1. Swapping the rectangle digits gives R1C1=1, R1C2=6, R4C2=1, R4C1=6. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.

Completing the corner with R4C1=1 gives R1C1=6, R1C2=1, R4C2=6, R4C1=1. Swapping the rectangle digits gives R1C1=1, R1C2=6, R4C2=1, R4C1=6. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Completing the corner with R4C1=1 gives R1C1=6, R1C2=1, R4C2=6, R4C1=1. Swapping the rectangle digits gives R1C1=1, R1C2=6, R4C2=1, R4C1=6. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Step 4 · Do not complete the swappable rectangle

Placing R4C1=1 would complete a swappable rectangle with the three player-entered values. Remove R4C1=1; the player entries themselves remain unchanged.

Placing R4C1=1 would complete a swappable rectangle with the three player-entered values. Remove R4C1=1; the player entries themselves remain unchanged.
Placing R4C1=1 would complete a swappable rectangle with the three player-entered values. Remove R4C1=1; the player entries themselves remain unchanged.

What it allows

Placing R4C1=1 would complete a swappable rectangle with the three player-entered values. Remove R4C1=1; the player entries themselves remain unchanged.

Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.
Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.

Step-by-step example · Bottom right

This example starts from a saved intermediate position. Its candidates include earlier logical eliminations; they are not fresh automatic notes.

Blue: evidence. Green: conclusion. Crossed-out digits: eliminated candidates. R1C1 means row 1, column 1.

Step 1 · Where to look

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.

This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
This argument assumes the puzzle has exactly one solution. These four cells occupy two rows, two columns and two boxes. Swapping the two digits would preserve every region.
Step 2 · Identify the three player-entered values

The values R1C4=9, R1C5=4, R6C4=4 were entered by the player during solving; none is a given clue. The remaining corner is R6C5=9. Only player-entered values may participate in this swap.

The values R1C4=9, R1C5=4, R6C4=4 were entered by the player during solving; none is a given clue. The remaining corner is R6C5=9. Only player-entered values may participate in this swap.
The values R1C4=9, R1C5=4, R6C4=4 were entered by the player during solving; none is a given clue. The remaining corner is R6C5=9. Only player-entered values may participate in this swap.
Step 3 · Compare the two rectangle fillings

Completing the corner with R6C5=9 gives R1C4=9, R1C5=4, R6C4=4, R6C5=9. Swapping the rectangle digits gives R1C4=4, R1C5=9, R6C4=9, R6C5=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.

Completing the corner with R6C5=9 gives R1C4=9, R1C5=4, R6C4=4, R6C5=9. Swapping the rectangle digits gives R1C4=4, R1C5=9, R6C4=9, R6C5=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Completing the corner with R6C5=9 gives R1C4=9, R1C5=4, R6C4=4, R6C5=9. Swapping the rectangle digits gives R1C4=4, R1C5=9, R6C4=9, R6C5=4. Both fillings preserve every row, column, and box, so allowing the completion would create two solutions.
Step 4 · Do not complete the swappable rectangle

Placing R6C5=9 would complete a swappable rectangle with the three player-entered values. Remove R6C5=9; the player entries themselves remain unchanged.

Placing R6C5=9 would complete a swappable rectangle with the three player-entered values. Remove R6C5=9; the player entries themselves remain unchanged.
Placing R6C5=9 would complete a swappable rectangle with the three player-entered values. Remove R6C5=9; the player entries themselves remain unchanged.

What it allows

Placing R6C5=9 would complete a swappable rectangle with the three player-entered values. Remove R6C5=9; the player entries themselves remain unchanged.

Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.
Avoidable Rectangle · Remove the candidate that would complete the deadly rectangle.

Practice

This course is adapted from Platon Sudoku App. Read the complete example here, then continue learning and practising in the app.

View on Google Play