What's My Number?

Discrete Mathematics Level 2

Calvin's favorite number \(N\) has the following properties:

  1. \(N\) has 8 distinct digits.
  2. The digits of \(N\) are strictly decreasing from left to right.
  3. \(N\) is divisible by 180.

What are the first three digits of Calvin's favorite number?

This problem is posed by Muhammad A.

Details and assumptions

The first three digits of \(1023\) are \(102\). Ignore any leading zeroes.


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