1. Sally is thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000. What number was Sally thinking of?

2. This is a variation on a classic "guess the numbers" puzzle: 

I think of 2 single-digit numbers from 1 to 9.  I tell Peter Griffin their product and Lois Griffin their sum.

Peter: "I don't know the numbers."
Lois: "I don't know the numbers."
Peter: "I don't know the numbers."
Lois: "I don't know the numbers."
Peter: "I don't know the numbers."
Lois: "I don't know the numbers."
Peter: "I don't know the numbers."
Lois: "I don't know the numbers."
Peter: "Now I know the numbers."

What are the numbers?

Source: unknown

3. Find three three-digit square numbers that together use each of the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 exactly once.