Hi Waiyan,
There is actually more than one solution to this riddle. I am not going to give you an answer but I can give you some hints to find it.
Using 1 9, the 4 digit numbers will range from 1234 to 9876. Since the largest product is 9876, the largest 4 digit multiplicand will be 4939 and the smallest can be 1234.
The single digit multiplicand can only be 2, 3, 4 , 6 or 7 for the following reasons:
 any number multiplied by 5 will end in 0 or 5
 any number multiplied by 8 must be smaller than 1232 or the product will be greater than 9876. This is smaller than the smallest possible multiplicand.
 any number multiplied by 9 must be smaller than 1097 or the product will be greater than 9876.This is smaller than the smallest possible multiplicand.
The four digit multiplicand
 cannot end in 1, since then the product will be the same as the single digit multiplicand.
 if multiplied by 7 cannot be greater than 1398
 if multiplied by 6 cannot be greater than 1598
 if multiplied by 4 cannot be greater than 2398
 if multiplied by 3 cannot be greater than 2987
 if multiplied by 2 cannot be greater than 4938
Guess and check is the only way to solve this question but that doesn't mean you can't make an educated guess. Using a spreadsheet would also will help you find your answer quicker.
Good luck finding your solution,
Janice
