Question 10
A pair of positive integers is called compatible if one number equals the sum of all digits in the pair and the other equals the product of all digits in the pair. Find all pairs of positive compatible numbers less than $100$ (5 marks).
Investigation (3 bonus marks, separate from the base score): find all pairs of positive compatible numbers less than $1000$ with at least one number greater than $99$.
Investigation (3 bonus marks, separate from the base score): find all pairs of positive compatible numbers less than $1000$ with at least one number greater than $99$.