#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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