#math trivia #133 solution

#math trivia for #May12:  #133 has the form xyz where xyz is one more than a multiple of yz (133 = 4*33+1).  Which other day-numbers do?

Answer:  If xyz is one more than a multiple of yz, then x00 = xyz = yz is also one more than a multiple of yz.  This means that yz must be a divisor of 99, 199, or 299.  We should therefore look at one- and two-digit divisors of these three numbers, which are:

  • 99:  1, 3, 9, 11, 33
  • 199:  1
  • 299:  1, 13, 23

This leads to the following solutions, based on the value of yz:

  • 01:  01, 101, 201, 301
  • 03:  103
  • 09:  109
  • 11:  111
  • 13:  313
  • 23:  323
  • 33:  133

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