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  2. Missing square puzzle - Wikipedia

    en.wikipedia.org/wiki/Missing_square_puzzle

    With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square. The amount of bending is approximately ⁠ 1 / 28 ⁠ unit (1.245364267°), which is difficult to see on the diagram of the puzzle, and was illustrated as a graphic. Note the grid point where the ...

  3. Square packing - Wikipedia

    en.wikipedia.org/wiki/Square_packing

    Square packing in a square is the problem of determining the maximum number of unit squares (squares of side length one) that can be packed inside a larger square of side length . If a {\displaystyle a} is an integer , the answer is a 2 , {\displaystyle a^{2},} but the precise – or even asymptotic – amount of unfilled space for an arbitrary ...

  4. Polyominoes: Puzzles, Patterns, Problems, and Packings

    en.wikipedia.org/wiki/Polyominoes:_Puzzles...

    Polyominoes: Puzzles, Patterns, Problems, and Packings is a mathematics book on polyominoes, the shapes formed by connecting some number of unit squares edge-to-edge. It was written by Solomon Golomb, and is "universally regarded as a classic in recreational mathematics". [1]

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  6. Vanishing puzzle - Wikipedia

    en.wikipedia.org/wiki/Vanishing_puzzle

    The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.

  7. Soma cube - Wikipedia

    en.wikipedia.org/wiki/Soma_cube

    Similar to Soma cube is the 3D pentomino puzzle, which can fill boxes of 2×3×10, 2×5×6 and 3×4×5 units. The Bedlam cube is a 4×4×4 sided cube puzzle consisting of twelve pentacubes and one tetracube. The Diabolical cube is a puzzle of six polycubes that can be assembled together to form a single 3×3×3 cube.

  8. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    People are given n unit squares and have to pack them into the smallest possible container, where the container type varies: Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5).

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