There is a seven digit number N, with unique digits (that is, there are no repeats), and the interesting property that N is evenly divisible by each of its digits D.
Clarification from the puzzle master: We are not saying that if a digit D evenly divides N, then D must be one of the digits of N. In other words, although the digit 1 will surely divide N, that doesn't guarantee that 1 is one of the digits. Logically, even division is necessary, but not sufficient.
Puzzle #1: From these conditions, it is possible to determine what the digits of N must be. What are they?
Puzzle #2 is: Perhaps N is not unique, but can you give at least one example of such a number?
I give up, let me see the solution.