#math trivia #124 solution

This is a little different than the answer to #123, where the digits had to be in increasing order.  (And to be clear, the “the” in “the no” is an error; it should be “that no digit …”.)  The hundreds and the tens digits can be equal to the ones digit, they just can’t be larger.

The possibilities are as follows:

  • 1-9:  all 9
  • 10-99:  all of the form xy where y >= x:  9+8+7+6+5+4+3+2+1 = 45
  • 100-199:  all of the form 1xy where y >= x and y >= 1:  9+9+8+7+6+5+4+3+2+1 = 54
  • 200-299:  all of the form 2xy where y >= x and y >= 2:  8+8+8+7+6+5+4+3+2+1 = 52
  • 300-366:  all of the form 3xy where y >= x, y >= 3, and xy <= 66:  7+7+7+7+6+5+1 = 40

The answer is 200.  More than half of the day-numbers have the property.

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