Find the adjacent tiles
Name every tile that can slide into the blank, then finish the board. A diagonal neighbour does not count.
PRACTICE COLLECTION
Sliding Tiles — Foundations: read the board before moving
Four studies in legal moves and their immediate effects. Make a prediction, test it, and compare the starting-position answer.
Print these four studies with answers
Use a prediction, a test and a reason
- Read the task before opening the answer. Say where a move lands or what it changes.
- Test it on the playable board. In two-player studies, play both sides to inspect a reply.
- Undo and compare one alternative. Use the answer’s stated search limit when explaining the result.
- Repeat the decision on paper, where the move cannot be checked for you automatically.
These are teaching groups, not a player-tested difficulty ladder. The four board IDs match the technique examples, individual study pages and print pack.
Read a central blank
Name every tile that can slide into the blank, then finish the board. A diagonal neighbour does not count.
Make space before moving a tile
Plan the blank’s route before chasing a numbered tile. Compare the first moves, then find a shortest finish.
Route around displaced tiles
Plan the blank’s route before chasing a numbered tile. Compare the first moves, then find a shortest finish.
Bring the idea to a fresh round
A legal move need not improve a position. Local routes and cycles demonstrate their stated effects; they do not prove a globally shortest solution. A study's minimum-distance claim requires a search that has ruled out every shorter route from that exact position. It is not a promise about general scrambles. The parity test below applies to this four-by-four board and this particular goal. A route that preserves a solved region is useful only while enough space remains to execute it. Generated scrambles are reachable, but an arbitrary rearrangement supplied in a study may not be.
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