Efficiency means that you handle each tile as little as possible, and that you make as few mistakes as possible. Ideally you want to pick up a tile and fit it to at least one other rather than put it down again unmatched. Incorrect fitting wastes time when correct matches are rejected and when you have to unpick the mistake.
From experience, the most efficient strategy has 5 stages. Overall this strategy is : (i) divide the problem into manageable sub-tasks, and (ii) do the easiest tasks first. The goal is to minimise the choice of tiles and maximise the number of clues at each stage, particularly for the hardest tasks.
In the early stages colour and pattern are important, because these features are the most easily identified and distinguished. In the last stage when remaining tiles are almost identical in colour, shape becomes the dominant distinguishing feature.
- Turn all tiles face up and sort them into about 6 groups. One group is all edge tiles. Another group is the skyline. Other groups are the major colours or combinations of colours in the picture. Examples are : sky, sea, foliage, flowers, buildings, roads, people/animals. Then separate out tiles belonging to individual features within each group, in preparation for stage 2.
There should be no assembly until stage 1 is complete, because assembly is easiest when all the required tiles are at hand.
- Assemble small clusters of high-contrast patterns and easily distinguished features within each group. Typical features are faces, groups of people, windows, doors, chimneys, printed signs, the skyline, the outlines of buildings. This is your strategy #3. Regions which are mostly featureless such as the sky, or which can only be distinguished in the fine detail such as foliage, should be left to stage 5.
Assembling the border early on provides a framework for placing clusters in their approximate positions.
Extend the small clusters outwards by fitting as many as possible of the remaining tiles from the same colour group. At this stage it is efficient to pick up the most distincitive tile, locate it on the picture, and then place it in its exact place in the correct cluster, like a golfing hole-in-one. This is efficient because you are almost certain to connect it to a cluster, or at least place it beside a cluster. The reverse strategy is also efficient : use the picture and the shape of the gap to identify the missing tile among those remaining. This stage overlaps with the next :
Join the small clusters together and attach them to the borders. This requires looking for the matching of patterns and colours and also the interlocking of shapes at large scales (clusters) and at small scales (individual knobs and holes).
Fill in the remaining gaps. Start by completing the picture-matching strategy of stage 3, extending outwards the most easily identified features or patterns, which have the smallest choice of alternatives. Leave until last the largest areas of featureless, uniform pattern or colour, such as the sky, sea, foliage, grass, or dark shadow. These require the laborious testing of numerous options. This is your strategy #1.
The last stage requires the most organisation, method and attention to detail. Sort the pieces into 5 rows of tiles with 4 knobs down to none, with each row sorted from light to dark. Identify gaps in the puzzle where there are 2 or 3 adjacent tiles, or which have unusual shapes or the fewest remaining tiles of that shade of colour. These give the most confidence of a correct fit, and are the easiest to find.
At each stage (particularly the last) it is important to make full use of all the clues available in order to ensure that the fit is correct : check the exact match of colour and patterns and also the ease with which the tiles fit together. A fit which is too tight or too loose, or leaves an uneven gap around a tile, is almost certainly wrong.
Beside the picture, the pattern in the shapes of tiles is also a clue, to ensure that a fit is correct, or narrowing the search for a tile. In most jigsaw puzzles four tiles meet at every corner, and there is a repeating pattern of wide or narrow tiles every 6-8 rows or columns.
The above strategy - or one very close to it - is mentioned in most online advice. For example :
HobbyLark : How To Do Jigsaw Puzzles Like an Expert
Puzzle Warehouse :Jigsaw Puzzle Stragegies - A Guide to becoming a Puzzle Expert
wiki : How to Assemble Jigsaw Puzzles
Quora : How does one solve a jigsaw puzzle in the fastest way possible?
Chapter 1 : The Jigsaw Puzzle Problem (a thesis examining automation of solution strategies)
I agree with other answers here that your strategies #2, #4 and #5 are inefficient and should be avoided.
Strategy #2 : Starting from one corner can be useful when the only clue is the shape of the pieces. But generally this requires laborious searching and checking of a large number of possible options, which should be left until the options have been narrowed down (stage 4).
Strategy #4 : It is satisfying to pick up an interesting tile, locate it on the picture, and then fit it at once into its exact position in the puzzle. However, this is only likely to succeed when adjacent tiles are already in place.
Strategy #5 : Trying to fit random tiles together is highly inefficient. You are very unlikely to get a match because there are very many options, and you might try the same tiles more than once.
