Divide by Box, decoded
Divide by Box is the name several puzzle apps use for the Japanese classic Shikaku (Nikoli, 1989) — the same game English publishers also call Rectangles. Whatever the label, you're doing one thing: dividing a grid into boxes so that each box contains a single number, and that number equals exactly how many cells the box covers.
The board above is the real thing, not a screenshot — drag from one corner to the opposite corner and the box snaps to the grid, with a live count of the cells you've enclosed. Draw a box with the wrong area and it turns red until you fix it; get it right and its number dims. Fill the whole grid with correct boxes and the puzzle is solved.
The thinking behind the boxes
Good Divide by Box play is about asking, for each number, "where can this box go?" — and noticing when the answer is "only one place." The number 9 in a corner might allow just a 3×3 square. A 2 wedged between two other numbers may have a single free neighbor. On our medium and hard tiers you'll also use overlap logic: when every possible box for a number covers some particular cell, that cell is spoken for, and every other number must plan around it.
Each of our boards — the shared daily, the archive, and the 600-plus puzzle collection from 5×5 to 20×20 — is machine-verified to have exactly one solution, so a forced move always exists and guessing is never required.