How to Solve Star Chart: Four Techniques

Star Chart hides a fixed number of stars on a square grid and gives you numbers to find them with. Each numbered cell counts the stars sitting in the eight cells that touch it, and a numbered cell never holds a star itself. You rule out the cells you’ve eliminated and place stars on the ones you’ve proved. Every puzzle has exactly one solution, and every step toward it is a deduction rather than a gamble. Try these techniques out on the Star Chart board.

The difference from Minesweeper matters. There the numbers appear as you click, so the opening move and some endgame positions are coin flips. In Star Chart every clue is visible before you touch anything; all the information you will ever get is already on the board.

Four techniques cover the whole game, and they line up with the difficulty tiers. An easy board (7x7, ten stars) falls to the first one alone. A medium board (9x9, sixteen stars) needs the second and the star counter as well. A hard board (11x11, twenty-four stars) needs all four. The puzzles are generated to guarantee that, so being stuck on an easy board means a single-clue count has been missed.

Technique one: count a single clue

Almost every move comes from one clue considered on its own, and it works in two directions.

If a clue’s stars are all found, every remaining undecided neighbour is empty. A “2” with two stars already beside it has met its quota, and the rest of its neighbourhood clears in one sweep.

If a clue’s undecided neighbours number exactly as many stars as it still needs, all of them are stars. A “3” with one star placed and two undecided neighbours left needs both of them.

Start at the corners and edges. A corner cell has three neighbours instead of eight, so both halves of the count trigger far sooner there. Re-check every clue next to a cell you just decided; one placement often satisfies two or three clues and cascades.

This technique alone solves every easy puzzle.

Technique two: read two clues against each other

Medium boards reach a position where no single clue resolves: every number has more undecided neighbours than it needs stars, and fewer than it would take to force them all. Compare two clues instead.

The useful case is nesting. When one clue’s undecided cells sit entirely inside another’s, subtract the numbers, and the difference is how many stars live in the cells that only the larger clue covers.

Here is a position on the top edge of a board, with nothing around the two clues decided yet:

      a   b   c
 r1   ?   1   ?     <- r1 is the top row of the board
 r2   ?   4   ?
 r3   ?   ?   ?

The “1” at r1b sits on the top row, so it has five neighbours rather than eight: r1a, r1c, r2a, r2b and r2c. One of those, r2b, is the “4” itself, and clues never hold stars, so four undecided cells surround the “1”.

The “4” at r2b has all eight neighbours. Drop r1b, which is the “1” and therefore empty, and seven undecided cells remain: the same four, plus r3a, r3b and r3c.

Neither clue resolves alone, since the “1” needs one star among four cells and the “4” needs four among seven. The “1” cells are a subset of the “4” cells, though, so exactly one star sits somewhere in the four shared cells, which leaves 4 − 1 = 3 stars for the cells only the “4” covers. There are exactly three of them, so r3a, r3b and r3c are all stars.

The four shared cells stay unresolved. Subtraction tells you about the difference between two clues, not about their overlap.

Nesting shows up most often between clues one or two cells apart, and between a border clue and one just inside it. It also appears mid-solve, once ruled-out cells shrink one clue’s undecided set into another’s, so re-scan neighbouring pairs after every batch of eliminations.

Technique three: use the star counter

The remaining-stars number at the top of the board is a clue like any other, and it’s the one players forget. It constrains the whole grid rather than a neighbourhood, which makes it weak early and decisive late.

Two direct uses: when the remaining count equals the number of undecided cells on the board, all of them are stars, and when it reaches zero, every undecided cell is empty.

The sharper use is regional. Late in a puzzle the undecided cells split into separate pockets. If the clues around one pocket pin down how many stars it holds, subtract that from the counter and the rest belongs to the other pockets. On medium boards this often turns a stalled position into a finish.

Technique four: try a clue’s possibilities

Hard boards contain at least one position where none of the above moves. The technique that breaks it is enumeration, still deduction rather than guessing.

Pick a clue with few undecided neighbours and a small number, since that admits the fewest arrangements. A “2” with four undecided neighbours has six; a “1” with three has three. List them all. For each one, check the neighbouring clues, and discard any arrangement that pushes a nearby clue above its number or leaves it unable to reach its number with the cells it has left.

Compare what survives. A cell holding a star in every surviving arrangement is a star, and a cell empty in every one is empty. Cells that differ between survivors stay undecided.

This is slower than the other three, so reach for it last. Hard boards usually need it once or twice, and one resolved cell reopens the cheaper techniques.

The three lives are the point

Three wrong stars end the round. That constraint is what keeps probing from replacing reasoning: with unlimited lives the fastest strategy would be to click a plausible cell and watch what happens, and the logic would never need doing.

So treat uncertainty as an unfound deduction rather than a coin flip. Every puzzle is solvable by these four techniques without guessing, so a position that feels ambiguous has a move in it somewhere, usually a clue you counted before its neighbourhood changed or a nested pair you haven’t compared. Check the border clues first.

Star Chart is part of the Daily Puzzle rotation if you’d like a fresh grid each day, and how logic puzzles sharpen problem-solving covers what this kind of reasoning does and doesn’t train.