Alice's favorite number has the following properties:
[list]
[*] It has 8 distinct digits.
[*]The digits are decreasing when read from left to right.
[*]It is divisible by 180.[/list]
What is Alice's favorite number?

[i]Author: Anderson Wang[/i]
1. **Divisibility by 180**: 
   - Since Alice's favorite number is divisible by 180, it must be divisible by 2, 5, and 9 (since \(180 = 2^2 \times 3^2 \times 5\)).
   - For divisibility by 2, the number must end in an even digit.
   - For divisibility by 5, the number must end in 0 or 5. Since it must also be even, it must end in 0.
   - For divisibility by 9, the sum of the digits must be divisible by 9.

2. **Distinct digits and decreasing order**:
   - The number has 8 distinct digits, and they must be in decreasing order.
   - The digits are chosen from the set \(\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}\).

3. **Sum of digits**:
   - The sum of all digits from 0 to 9 is \(0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45\).
   - Since the number has 8 digits, we need to exclude 2 digits such that the sum of the remaining 8 digits is divisible by 9.

4. **Finding the digits**:
   - If we exclude digits \(x\) and \(9-x\), the sum of the remaining digits is \(45 - (x + (9 - x)) = 45 - 9 = 36\), which is divisible by 9.
   - We need to ensure that the number ends in 0 and is in decreasing order.

5. **Excluding digits**:
   - To ensure the number ends in 0 and is in decreasing order, we need to exclude digits such that the remaining digits form a valid sequence.
   - Exclude 1 and 8: The remaining digits are \(\{0, 2, 3, 4, 5, 6, 7, 9\}\).

6. **Forming the number**:
   - Arrange the remaining digits in decreasing order: \(97654320\).

7. **Verification**:
   - The number \(97654320\) ends in 0 (divisible by 2 and 5).
   - The sum of the digits \(9 + 7 + 6 + 5 + 4 + 3 + 2 + 0 = 36\), which is divisible by 9.
   - The number is in decreasing order and uses 8 distinct digits.

Thus, Alice's favorite number is \(\boxed{97654320}\).