Shape & Sliding Puzzles
Two related problems live here: fitting shapes into a space they exactly fill, and sliding tiles until they are in the right order. Tangram sets, pentomino boards, hex grids and the classic scrambled-picture slider.
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Shape-fitting is the older idea. A tangram gives you seven pieces and an outline they fill precisely, with no room for approximation — either the arrangement is right or it is not. Pentominoes work the same way with twelve pieces made of five squares each, and both share the property that makes the format satisfying: the solution is provable, not merely acceptable.
Sliding boards look easier and often are not. A scrambled picture in a four-by-four frame has fifteen tiles and one gap, and everything you do has to pass through that gap. The last two tiles are the famous difficulty — they cannot be placed independently, and getting them right means temporarily unmaking part of what you have already solved.
Hex boards are the newest of the three and change the geometry rather than the goal. Six directions instead of four means a piece has more places to go and more ways to block itself, which makes planning two moves ahead genuinely harder rather than just longer.
Nothing in this section is timed by default. These are problems with answers, and rushing one is mostly a way of arriving at the wrong answer sooner.
Questions about this section
What is the difference between a tangram and a pentomino board?
A tangram uses seven pieces of mixed shapes to fill an outline; pentominoes use twelve pieces each made of five squares. Both demand an exact fit rather than a close one.
Why are the last two tiles of a sliding puzzle so hard?
Because they cannot be placed one at a time — solving them means partly unmaking the row above and rebuilding it with both in position.