Modern combinatorics reveals that the number of ways to place the pieces of the Suter board to reform their square, allowing them to be turned over, is 17,152; the number is considerably smaller – 64 – if pieces are not allowed to be turned over. The sharpness of some angles in the Suter board makes fabrication difficult, while play could be awkward if pieces with sharp points are turned over. For the Codex board (again as with Tangram) there are three ways to pack the pieces: as two unit squares side by side; as two unit squares one on top of the other; and as a single square of side the square root of two. But the key to these packings is forming isosceles right triangles, just as Socrates gets the slave boy to consider in Plato's Meno – Socrates was arguing for knowledge by recollection, and here pattern recognition and memory seem more pertinent than a count of solutions. The Codex board can be found as an extension of Socrates' argument in a seven-by-seven-square grid, suggesting an iterative construction of the side-diameter numbers that give rational approximations to the square root of two.
Modern combinatorics reveals that the number of ways to place the pieces of the Suter board to reform their square, allowing them to be turned over, is 17,152; the number is considerably smaller – 64 – if pieces are not allowed to be turned over. The sharpness of some angles in the Suter board makes fabrication difficult, while play could be awkward if pieces with sharp points are turned over. For the Codex board (again as with Tangram) there are three ways to pack the pieces: as two unit squares side by side; as two unit squares one on top of the other; and as a single square of side the square root of two. But the key to these packings is forming isosceles right triangles just as Socrates gets the slave boy to consider in Plato's Meno – Socrates was arguing for knowledge by recollection, and here pattern recognition and memory seem more pertinent than a count of solutions. The Codex board can be found as an extension of Socrates' argument in a seven-by-seven-square grid, suggesting an iterative construction of the side-diameter numbers that give rational approximations to the square root of two.