What is the least-four digit number with no repeated digit?

Answer 1

The key in this type of problems is to advance from left to right, and to use the smallest possible digit in each case. Thus, the first digit (from the left) has to be a one, since a number doesn't start with a zero; the next digit has to be a zero; etc.

Answer 2

0123 or 1234 - depending on whether you allow the first digit to be zero