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?

If there were only two numbers, then the minimum looks like it is

1*23456789 = 23,456,789

So I guess that the minimum with 4 numbers is

** 1*2*3*456789 = 2,740,734**

Moving any digit from the long number to one of the short ones seems to increase the short one by more than it decreases the long one, percentagewise

For instance, move the 5 to behind the 3

35/3 ~= 11.67

but 46789/456789 ~= 1/9.76

So 1*2*35*46789 is bigger by about 11.67/9.76 = 120%

So, I wouldn't be surprised if my first guess was right.

(I also wouldn't be too surprised if it was wrong)