Third in a series with puzzle solving tips. This time, a dissection of Saturday’s Star Battle.
Jack Bross left an excellent set of starting tips for Star Battle in Dr. Sudoku Prescribes #14 so if you are struggling with these puzzles, start there. The hard Saturday puzzle required some unusual group recognition which I thought deserved to be highlighted.
The Boxed In theme comes from these sub-groups of regions.
It is usual to count up boxes in rows or columns to figure out extra/left-over stars. But this geometry allows the whole puzzle to be split into 4×4 regions with either 2 or 4 stars as shown below. This is because the 4×4 corner that is not part of each 4×8 rectangle has a fixed number of stars and you can work out from there. Having these counts in mind, particularly in the very upper-right corner, will be key to make progress in the puzzle.
A first pass at the puzzle with this knowledge should place these almost stars and gray out these impossible to use cells. Not all of these deductions are trivial but you should think your way through any grayed out cell that seems unusual to you.
There are two key spots to make progress in, both marked in orange. In the upper-right 4×4 square there must be 4 stars. Notice how filling in the orange cell would prevent there being 4 stars in this subregion so it can be excluded. This now places 2 stars in the top row and blanks out the rest of it, which sets it up for a future deduction.
A “push” logic works on the bottom. Often, when you have two stars almost placed close together, putting one in a specific place will push the other into a specific place too. Notice that putting a star in the orange cell places another in the bottom row (now for 3 total stars in that row). That isn’t allowed, so that star must be in the 4th column and now you can place other stars into the 3rd column as the 4th is filled. Keep doing this and you should be able to get a lot of the stars placed as in this image.
The final steps come from remembering you need 4 stars in the upper-right, which moves both orange stars over to the right. To finish, try to complete the 4th row up top, and try to complete the 5th column in the bottom, with the basic eliminations you can now perform. Master the art of “push” logic and counting up regions and subregions and you’ll get much faster at these challenging Star Battle puzzles.