#math trivia #263 solution

The base-N representations of 263 for N = 2, …, 9 are:

  • 100000111 base 2
  • 100202 base 3
  • 10013 base 4
  • 2023 base 5
  • 1115 base 6
  • 524 base 7
  • 407 base 8
  • 322 base 9

The representations that don’t include at least one of the digits in 263 are N = 2, 6 and 8.  In addition, if we count unary representation (which is sometimes considered base-1), then the representation for N = 1 doesn’t include one of the digits either.  (The unary representation of 263 consists of 263 1’s.)

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