Each of P, Q, R and S together uses the base ten digits from 1 to 9 exactly once.
What are the respective minimum and maximum value of P*Q*R*S?
Here, I think that we want the numbers to be close together. So we have a 3 digit number and three 2 digit numbers.
I guess that the three digit number starts with a 9 and the others start with 8, 7, 6. I guess that they are followed by 5, 4, 3 and 2, in reverse order.
First intuition, therefore, is 921*83*74*65 = 367,690,830.
I am less confident about this guess. It is based on the well-known result that if two numbers have a constant sum, then their product is increased if they are closer together.
So, for instance, 74*65 < 76*64. Which is why I assigned the digits 5,4,3 and 2 in reverse order.