How to sort puzzle pieces by shape
To sort puzzle pieces by shape, group outward tabs and inward blanks by both their number and their arrangement. Then read the connectors a particular gap needs and search only compatible candidates. Shape sorting is especially useful within a plain area, not necessarily across the whole box.
Start with the area you are trying to fill
Keep sky pieces with sky, water with water and background pieces with their likely background before sorting by outline. Combining every colour into one shape sort usually leaves you with many irrelevant candidates. The picture still helps, even when its clues are faint.
Lay that smaller group picture side up in shallow trays or rows. Keep boundary pieces visible: a sliver of a cloud, horizon or roof may make a piece easier to locate than an entirely plain one. Deal with edges separately because their straight sides give different clues from inner pieces.
Name the connectors: tabs and blanks
A tab is an outward connector, sometimes called a knob. A blank is an inward curve, also called a socket or hole. For regular four-sided inner pieces, useful groups include one tab and three blanks, two tabs and two blanks, three tabs and one blank, and any all-tab or all-blank pieces present.
These are sorting categories, not a promise that your puzzle contains every type. Some puzzles have very similar outlines throughout, while irregular-cut puzzles may not have four obvious sides. Use the actual features of your pieces instead of making them fit a diagram that doesn't apply.
Separate adjacent tabs from opposite tabs
Two tabs beside each other make a different layout from two tabs across from each other. Put those two-tab arrangements in separate groups. A piece with adjacent tabs can't become an opposite-tab piece by rotation, so this distinction can rule out candidates immediately.
Turn a piece on the table to compare its arrangement with the opening. Keep its picture side up; turning it over reverses the view and hides the image clues. Splitting the group reduces irrelevant trials, but the amount depends on how many pieces of each layout your particular puzzle contains.
Read a gap before reaching for a candidate
Choose a gap with several neighbours already placed. If the neighbour above has a tab protruding down into the opening, the missing piece needs a blank on top. If the left neighbour has an inward socket facing the opening, the candidate needs a tab on its left.
Write down or remember the known sides before searching. Two known sides can narrow a group, but don't necessarily establish the whole outline: the unseen sides may still vary. A more enclosed gap gives you more constraints, so move to one of those if an open area leaves too many possibilities.
Compare connector position, width and curves
Within a compatible group, look at the actual outline. A tab close to one corner is different from a centred tab. Compare neck width, the depth of a blank and the broad curves of the piece. These details can eliminate a candidate before you try joining it.
For example, a gap may require two adjacent tabs, but also be noticeably narrow between its left and right neighbours. Start with compatible narrow pieces rather than testing every two-tab piece. Do not use pressure to overcome a width mismatch; a near-fit isn't made correct by pushing.
Keep colour and texture in the search
Even plain areas may contain a faint cloud edge, a change in shade or a printed grain. Compare these clues within each shape group. If the reference shows a clear light-to-dark change, arranging relevant candidates by shade may help; it isn't useful if the image has no such pattern.
Check the direction of a ripple or line after rotating a candidate. The connectors can match while the image points the wrong way. In repeated patterns, check continuity across several seams rather than trusting a single matching colour.
Test systematically and recheck assumptions
For one gap, keep tried pieces to one side so you don't repeatedly test them. When you move to a different gap, those pieces become candidates again; they have only been ruled out for the specific opening you checked.
If none fits, reconsider the location of the group and inspect neighbouring joins for false fits. A piece should lie level without force and carry the image across the seam. If shape gives too few clues, build another area or use the reference picture before returning. Sorting is a way to reduce searching, not a guarantee that every remaining piece will become obvious.
Questions
Should I sort the whole puzzle by shape first?
Usually start with useful picture groups, then shape-sort the area that needs it. For a very uniform image, a broader shape sort may be practical, but there is no required order.
Does this work for random-cut puzzles?
Use distinctive outlines and connector positions on irregular pieces. The regular four-side tab-count categories may not apply.
What is the difference between adjacent and opposite tabs?
Adjacent tabs sit on neighbouring sides; opposite tabs sit across the piece from each other. Rotating a piece doesn't change that relationship.