AMC 8 Daily Practice Round 9

We classify the four-digit numbers into four cases:

① All four digits are the same. Possible numbers:

Total: numbers.

② Two different digits appear twice each. For example, numbers like .

We choose two different digits from , which can be done in ways.

Each choice allows different digit arrangements, so this case contributes:      

③ Three different digits appear, with one digit repeated. Examples include .

The valid digit sum conditions are and , giving valid digit sets.

Each set allows different digit arrangements, so this case contributes:

④ All four digits are different. Valid numbers include , totaling:      

Adding all cases together:  

The answer is .