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.
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The largest ten digit number with no repeated digits is '9876543210'.
The greatest 4-digit number with no repeated digits is... 9876
9876
1023456789
123456.