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10×10 Star Battle puzzles

3,500 10×10 boards on this site, 1,500 of them two-star. Play one now — pick 10×10 and a difficulty.

What a 10×10 board asks for

One star per row, column and region. A 10×10 grid is divided into 10 regions and takes 10 stars in total — one in every row, one in every column, one in every region, and no two of them touching, not even at a corner. 2,000 boards, with 6.1 named techniques needed on an average one.

Two stars per row, column and region. The same 10×10 grid, but every row, column and region needs a pair. That is 20 stars on the same number of cells, which is a different puzzle rather than a harder one: a region can hold a star and still be owed another, so where the second one must go becomes an argument you can make. 1,500 boards, with 8.3 named techniques needed on an average one.

How hard they get

The rating comes from the solver: it adds up every step a board needs, and harder kinds of step count for more. Nothing is filled in at the start of any board, so a hard one is hard because its reasoning is longer and trickier.

  • 2,000 one-star: 141 easy, 828 medium, 703 hard, 328 expert
  • 1,500 two-star: 229 easy, 371 medium, 382 hard, 518 expert

Different techniques per level

How many different techniques a board needs on average, at each level. The rating is not this count: it weighs every step, so a higher level can need the same number of different techniques, or even fewer.

  • One star: easy 5.3, medium 6.2, hard 6.2, expert 6.1
  • Two stars: easy 7.2, medium 8.5, hard 8.4, expert 8.5

Which techniques a 10×10 board needs

Measured across every board in the pack, not estimated. A technique counts once per board, however many times it fires.

One star:

Two stars:

  • Only enough room left — 100% of boards. Whenever eliminations have narrowed a row, column, or region down to just enough cells.
  • Stars cannot touch — 100% of boards. Immediately after placing any star.
  • A full line is closed — 100% of boards. After placing the last star a row, column, or region was owed.
  • Cells with no room around them — 100% of boards. At the very start of a two-star puzzle, and any time a region owing two or more stars looks cramped. It is usually the first move available on an empty grid.
  • Cells caught between candidates — 99% of boards. When a row, column, or region is down to two or three open cells sitting close together.
  • Checking a region case by case — 85% of boards. When nothing else is moving, and some region is down to a handful of open cells with only a few sensible ways to fill them.
  • Several regions filling the same rows — 77% of boards. When two or three regions are each squeezed into the same small band of rows or columns, and no single one of them is confined on its own.
  • A region trapped in a row or column — 71% of boards. When every open cell of a region sits in the same row, or in the same column, or spans just two of them.
  • Counting across two neighbouring rows — 58% of boards. On two-star puzzles, whenever two side-by-side rows or columns are still short of stars and the open cells are bunched together.
  • A row trapped in a region — 36% of boards. When every open cell of a row or column belongs to one region, or to just two.

Every one is explained, with an example, on the techniques page. A board is published only once it is checked to have exactly one solution that these techniques can reach, so no size ever needs guessing.

How this compares with the other size

A 10×10 board needs 7.2 different techniques on average; an 8×8 one needs 5.9. So this is the longer think of the two, and 8×8 is the better place to start.

Other sizes