All thinkers

W. T. Tutte: 2 puzzles worth knowing

2 puzzles from W. T. Tutte, each explained in a minute and credited to the original work. Free on Savvy.

• Can a square be sliced into smaller squares, no two the same size, with none left over?

  Cut a large square into smaller squares — every piece a square, no two the same size, and no wasted space. Mathematicians call this 'squaring the square,' and for decades no one co…

  — Brooks, Smith, Stone and Tutte; popularized by Martin Gardner, Squared square

• Tile a square with smaller squares, no two the same size, none left over

  Can a square be divided into a finite number of smaller squares, using every size only once, with no gaps or overlaps? For decades mathematicians weren't even sure it was possible.

  — R. L. Brooks, C. A. B. Smith, A. H. Stone, and W. T. Tutte, The Dissection of Rectangles into Squares

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