Solving Problems by Eliminating Impossible Cases

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.

Problem

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

Solution

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 × 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

How Many Zeros Are There in n factorial

How many trailing zeros are there in 100! (! is read as factorial)? This is one of the most common problems in elementary school and middle school math competitions and for those who have memorized the strategy, this can be solved in less than five seconds. There are (100/5) + (100/25) = 24 trailing zeros in 100!. But why does the trick works?

Small Cases

Example 1: How many zeroes are there in 6!?

For those who are new to the factorial notation, when we say 6!, we mean that we multiply 6 and 5 and 4 all the way down to 1. That is

6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720.

So, where did all the zeros come from? Zero came from 5 multiplied by any even number factor. For example, in 6!,  if we multiply 6 and 5, this will give us 30, a number with one trailing zero. Notice that none of the remaining numbers in the multiplication can add another trailing zero. » Read more

The Math Word Problem Series on Number Problems

Below is the Number Word Problem Solving Series among the Math Word Problem Series in Math and Multimedia. In this series, several strategies were discussed on how to solve number problems.

1. How to Solve Number Problems Mentally

2. How to Solve Number Problems Using the Model Method

3. How to Solve Number Problems Using Algebra Part 1

4. How to Solve Number Problems Using Algebra Part 2

5. How to Solve Number Problems Using Algebra Part 3

In the next series, we are going to learn how to solve numbers involving age problems.

If you have questions or comments, please use the comment box below.

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