3. I'm thinking of a particular integer. It is a multiple of three, five, and seven. No digit occurs more than once. Can you find my number?
With that information there are lots of possibilities, so let me narrow the problem down with a few more clues.
- The digit in the tens place is a square number.
- The digits in the hundreds place is a cube.
- The digit in the hundred thousands place is both a square and a cube.
- Only the digit in the hundreds place is larger than the digit in the ones place.