Harry and Tom have each found a 4-digit perfect square, a 3-digit perfect cube and a 3-digit triangular number that use 10 different digits, but with no leading zero. A triangular number is one that ...

I have in mind three numbers. Each is a multiple of 3 and consists of three different non-zero digits, just one of which is 3. For each of these numbers individually, three of the following six ...