Shikaku: cells every option shares
When all of a number’s options cover the same cells, those cells are its. Every other number loses the options that use them.
How it works
Sometimes a number still has two or three options, but they agree on some cells. Whichever option is right, it covers those cells.
So those cells belong to that number, and no other rectangle can use them. Cross out every option of every other number that does. This often leaves a neighbour with one fit.
It is the same idea as the overlap rule in nonograms: push the rectangle every way it can go, and keep what all the positions share.
When nothing is shared
If every number’s options disagree everywhere, test one option honestly. Suppose it, then follow single fits and reach. If some number ends up with no option, or some cell with no number that can cover it, the option is out. That is a proof by contradiction.
Worth memorizing
Shared by every option means claimed.
Claimed cells knock out other numbers’ options.
Then look for a new single fit.
Practice
0 of 3 rightWhich cells do all the options of the ringed 5 share?
Which cells do all the options of the ringed 6 share?
Which cells do all the options of the ringed 3 share?