For readers playing Sudoku on Cool Math Games, this independent guide focuses on sudoku candidate notes. The examples teach stated local constraints, rather than presenting complete puzzles with proved unique solutions.
Candidate notes are useful only if you know what they represent. A small digit in a cell should mean that the digit remains possible under the constraints you have checked, not that you vaguely remember considering it.
A practical starting point
Keep notes consistent and update them after a confirmed placement. If a candidate disappears, be able to identify the row, column or box constraint that removed it.
Give pencil marks a consistent meaning
A note can represent a complete candidate set or a temporary reminder, but those are different conventions. Mixing them without a label makes deductions difficult to trust. When a confirmed number is placed, revisit affected candidates in its row, column and box. If you erase a candidate, be able to name the condition that excluded it. The examples supply their exclusions explicitly so that the set calculation can be checked independently of a larger puzzle.
A mistake to watch for
Do not mix complete candidate lists with partial reminders without a clear convention. An incomplete note can make a hidden single appear where none has been proved. The exercises state their candidate assumptions explicitly.
Worked examples and practice decisions
Try each question before reading its explanation. These examples are deliberately limited to the information they state. They separate a rule or calculation from a broader judgement about a complete game.
1. Candidate exercise 1: identify the forced digit
A row already contains [2, 4, 5, 7, 8, 9] and is missing [1, 3, 6]. For the target empty cell, its crossing column or box excludes [1, 3]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 6. The candidate set is therefore {6}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 6 is one member of the stated missing set [1, 3, 6]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
2. Candidate exercise 2: identify the forced digit
A row already contains [1, 2, 7, 8, 9] and is missing [3, 4, 5, 6]. For the target empty cell, its crossing column or box excludes [3, 4, 5]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 6. The candidate set is therefore {6}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 6 is one member of the stated missing set [3, 4, 5, 6]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
3. Candidate exercise 3: identify the forced digit
A row already contains [1, 2, 3, 4, 5, 9] and is missing [6, 7, 8]. For the target empty cell, its crossing column or box excludes [6, 8]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 7. The candidate set is therefore {7}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 7 is one member of the stated missing set [6, 7, 8]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
4. Candidate exercise 4: identify the forced digit
A row already contains [1, 2, 3, 5, 6] and is missing [4, 7, 8, 9]. For the target empty cell, its crossing column or box excludes [4, 8, 9]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 7. The candidate set is therefore {7}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 7 is one member of the stated missing set [4, 7, 8, 9]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
5. Candidate exercise 5: identify the forced digit
A row already contains [1, 3, 5, 7, 8, 9] and is missing [2, 4, 6]. For the target empty cell, its crossing column or box excludes [4, 6]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 2. The candidate set is therefore {2}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 2 is one member of the stated missing set [2, 4, 6]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
6. Candidate exercise 6: identify the forced digit
A row already contains [1, 2, 6, 8, 9] and is missing [3, 4, 5, 7]. For the target empty cell, its crossing column or box excludes [3, 4, 5]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 7. The candidate set is therefore {7}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 7 is one member of the stated missing set [3, 4, 5, 7]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
7. Candidate exercise 7: identify the forced digit
A row already contains [1, 2, 3, 5, 6, 7] and is missing [4, 8, 9]. For the target empty cell, its crossing column or box excludes [4, 8]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 9. The candidate set is therefore {9}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 9 is one member of the stated missing set [4, 8, 9]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
8. Candidate exercise 8: identify the forced digit
A row already contains [4, 5, 6, 8, 9] and is missing [1, 2, 3, 7]. For the target empty cell, its crossing column or box excludes [1, 3, 7]. These exclusions are explicitly supplied for this local exercise. Write the missing-digit set before selecting a final number. The order of the numbers in a set is not important; whether a candidate belongs to the set is what matters.
Intersecting the row’s missing digits with the crossing constraints leaves only 2. The candidate set is therefore {2}. This is a naked single for the target cell, provided the stated exclusions are correct. Record the candidate set before entering the final digit. If a later confirmed placement changes a unit, update the affected notes. Do not delete a candidate merely because it looks unlikely.
Countercheck: the target digit 2 is one member of the stated missing set [1, 2, 3, 7]. Choose another member and identify why it cannot replace the target under the supplied conditions. If you remove one of those conditions, reconsider whether the placement is still forced. This tests dependence on the evidence rather than on the appearance of the answer.
Use the guide in your next session
Practise the set calculation on paper before trying to do everything mentally. You can then compare the written candidates with the board rather than relying on a memory of an earlier position.
Begin with one observation connected to sudoku candidate notes. After checking an example, close the answer and reconstruct the reasoning in your own words. If a step is uncertain, return to that step rather than repeating a result you cannot explain. A small, specific correction provides a clearer next aim than trying to improve every part of a game at once.
Frequently asked questions
Are these complete Sudoku puzzles?
No. They are local constraint exercises with explicitly supplied exclusions. They do not establish the uniqueness of a complete grid.
Can a partial note prove a hidden single?
Not merely by omitting a digit elsewhere. A hidden-single claim needs the other locations to have been ruled out, not simply left unrecorded.
What should I check before entering a digit?
Check the cell’s row, column and box, and identify the constraint that removes every alternative candidate.
More cool math games guides
- Sudoku Beginner Guide: Rules, Units and First Deductions
- Sudoku Singles: Tell a Naked Single from a Hidden Single
- Open the relevant game or guide page
Sources and scope
This is an independent, AI-assisted editorial guide. The worked examples and diagrams are original teaching material, not official game screenshots or a claim of personal live-game testing. Game interfaces can change; check the current instructions when controls or rules differ.
