One of the strategies in solving problems is to divide them into cases and see if you can eliminate some impossible cases. In this post, I will discuss a popular classic problem which I found the solution to be interesting.
If A, B, C, and D are distinct non-zero digits, find their values if ABCD × 4 = DBCA.
If you have not encountered this problem before, you might want to solve it first before reading the solution below.
Finding the Value of A
One of the most obvious hints of the problem is that the value of A is only limited to 1 and 2. Why? Because if A is greater than 2, 4 × A will become a 2-digit number. This will make the product of ABCD × 4 a 5-digit number which does not satisfy the problem. » Read more