Learn Rectopia
Five ideas that solve every Rectopia board without guessing. They’re the same reasoning the hints use, put in plain words, roughly in the order you’ll reach for them.
1. Big patches first
Large numbers need lots of clear room, so they have the fewest places to go.
A big number needs a lot of clear space: a block that size, with no other clue inside it. On a crowded board there are rarely many such blocks, so the biggest clues often have only one or two ways to go. Small clues are the opposite, with lots of options until late.
Start by trying each big clue in every shape its number allows (a 12 could be 2×6, 3×4, 4×3 or 6×2) and crossing off the ones that hit the edge or another clue. Whatever’s left is short, and once a big patch is down, it boxes in everything around it.
2. Read the badge
A shape badge cuts a clue’s options down, and a numbered square has only one size.
The badge on a clue is its shape. A square badge with a number has exactly one size: a 9 square is 3×3, nothing else. A wide badge rules out every tall shape and the reverse, which halves the options. Corner brackets mean any rectangle, squares included.
Squares are the stiffest clues on the board, so look at them early. And a clue whose number is prime, like 5 or 7, can only be a single row or a single column of cells, whatever its badge allows.
3. Corners are decided
A corner cell has to be the corner of its patch, and usually only one clue can stretch that far.
A corner cell can only be covered by a patch that has that corner as its own corner. So ask which clues could stretch a rectangle all the way there without picking up a second clue on the way. Often only one can, and that settles who owns the corner.
The same thinking works along edges and in the nooks other patches leave behind. Any cell boxed in on two sides works like a corner: only a patch reaching it from the open side can cover it, and that’s usually a short list.
4. One clue per patch
A patch can never swallow a second clue, so neighboring clues fence each other in.
Every patch holds exactly one clue. That means a clue’s patch must stop before it reaches the next clue, so two clues side by side fence each other in. The space between them has to be split, never shared.
Use it to trim options fast. When you’re listing the ways a clue could go, throw out every rectangle that would contain another clue. On busy boards that alone can leave a clue with a single fit.
5. Mind the leftovers
Every cell needs a patch: a placement that strands a gap no clue can fill is wrong.
Every cell has to end up in some patch. After you place one, look at the empty cells it leaves around it. If a gap is too small, the wrong shape, or out of reach of every remaining clue, nothing can ever fill it, and that placement is wrong.
This is how to choose between two placements that both look fine. Try each in your head and check what it strands. The one that leaves a pocket no clue can cover is out. Near the end, the numbers left over have to add up to exactly the cells left over.
Try them out: play today’s daily or an unlimited game.