An example Counting Circles puzzle: each circled digit says how many circles hold it - three circles show 3, and one circle shows 1.
Counting Circles Sudoku draws circles on some cells with a wonderfully self-referential rule: the digit inside a circle equals how many circles on the whole grid contain that same digit. A circle showing 3 is telling you there are exactly three circles holding a 3 - itself included. Cells without a circle don't count at all.
The rule: the digit counts its own circles
Read any circled digit as a tally. If a circle holds 3, then across the grid exactly three circled cells contain a 3. If it holds 1, it is the only circle with a 1. Below, four circles read 1, 3, 3, 3 - consistent, because one circle holds the 1 and three circles hold a 3.
Four circles reading 1, 3, 3, 3: one circle holds the 1, and three circles hold a 3 - consistent.
A worked example, step by step
Suppose one circle is already known to be a 1.
Step 0. One circle is a 1; three others are unknown.
Step 1 - the 1 is unique. A circle of 1 says exactly one circle holds a 1. Since this circle is that one, no other circle can be a 1.
Step 1. The 1 is the only circle allowed to be a 1 - the others can't.
Step 2 - count the rest. The three remaining circles must be self-consistent: if one of them is a 3, then exactly three circles hold a 3, so all three must be 3s. The tally forces them together, and the whole set reads 1, 3, 3, 3.
Why the counting is so tight
Every circled digit is both a value and a constraint on the whole set of circles, so they lock into a small number of consistent patterns. A high digit like 8 is rare - it would need eight circles holding an 8 - while low digits appear in tight bunches (a lone 1, a pair of 2s, a trio of 3s). Counting the circles of each value is usually the fastest way in.
Solving strategy
- Read every circle as a tally. A digit d means exactly d circles hold d.
- Start with the 1. A circled 1 is unique - it bans that value from all other circles.
- Group the counts. Digits appear in bunches of their own size: one 1, two 2s, three 3s, and so on.
- Feed the grid. Each circled digit placed behaves like a given for its row, column and box.
Common mistakes
- Counting uncircled cells. Only circled cells count toward the tally - a 3 elsewhere is irrelevant.
- Forgetting the circle counts itself. A circle of 3 is one of the three 3s it refers to.
- Allowing too many. A digit d can appear in at most d circles - and must appear in exactly d.
- Ignoring ordinary Sudoku. Circled cells still obey their rows, columns and boxes.
Can I play it here?
Not yet - Counting Circles Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile:
- Browse all the Sudoku variants we do offer.
- Or print free puzzles from the printable PDF page.
Where to play it
Counting Circles Sudoku belongs to the misc family and runs on 9×9. It is not one SudokuStreak generates yet - but the deduction it trains is the deduction every Sudoku runs on.
Difficulty and type are two separate dials here: the type sets the extra rule, the level sets how much of the grid you start with. Expert Sudoku leaves 25 of the 81 cells filled, where the beginner tools dry up almost entirely; Evil Sudoku leaves 23, with no easy moves at all. Take it at the gentler end while the pattern is still new, and move up once it stops being a fight.