232 (number)

232 (two hundred [and] thirty-two) is the natural number following 231 and preceding 233.

232 is both a central polygonal number^[1] and a cake number.^[2] It is both a decagonal number^[3] and a centered 11-gonal number.^[4] It is also a refactorable number,^[5] a Motzkin sum,^[6] an idoneal number,^[7] and a noncototient.^[8]

232 is a telephone number: in a system of seven telephone users, there are 232 different ways of pairing up some of the users.^[9][10] There are also exactly 232 different eight-vertex connected indifference graphs, and 232 bracelets with eight beads of one color and seven of another.^[11] Because this number has the form 232 = 4⁴ − 4!, it follows that there are exactly 232 different functions from a set of four elements to a proper subset of the same set.^[12]

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