How many 3-digit numbers have a first digit which is triple the final digit?
I need to find all the 3-digit numbers of the form ABC, where A = 3C and B can be any digit from 0 to 9. I can start by listing the possible values of A and C: (3, 1), (6, 2), and (9, 3). For each pair of A and C, there are 10 choices for B, since it can be any digit. So the total number of 3-digit numbers that satisfy the condition is 10 times the number of pairs of A and C. There are 3 pairs of A and C, so the total number of 3-digit numbers is 10 times 3, which is 30. 