Digital Division

How many three digit numbers formed with three different digits from 0, 1, 2, 3 and 5 are divisible by 6?
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Problem



Consider all three-digit numbers formed by using different digits from 0, 1, 2, 3 and 5. How many of these numbers are divisible by 6?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.