Question

How many ways are there to add four positive even numbers to get a sum of 24

Answer 1

To find the way to add four positive even numbers to get 24, list possible combinations systematically, starting with the smallest even numbers and adjusting them while ensuring the total sum remains 24. This requires a basic understanding of even number properties and combinations.

Step-by-step explanation:

To find the number of ways to add four positive even numbers to get a sum of 24, we need to understand the properties of even numbers and use a systematic approach to identify all possible combinations. Since any even number can be written in the form of 2n where n is an integer, we recognize that the numbers we are dealing with are multiples of 2. We also know that the number 24 is an even number and can be divided by 2 to yield 12, which is our target sum when we express the problem in terms of n.

Let's consider different even numbers starting from the smallest positive even number, which is 2, and find possible sets of four such numbers that add up to 24. We can start by assuming one number to be the smallest, and systematically increase the value, checking every time whether the total sum is 24. For example, starting with (2, 2, 2, 18), we then change the last number to 16 and increase the one before it, getting (2, 2, 4, 16), and continue this process until we exhaust all possibilities.

Once we list all such possible combinations, we will find the total number of ways to add four positive even numbers to get a sum of 24. This combinatorial problem not only requires careful organization but also a basic understanding of number properties and combinations.

Answer 2

Based on the given conditions, there are a total of 11 ways to achieve this.

How to find the number of ways to add four positive even numbers to get a sum of 24

To find the number of ways to add four positive even numbers to get a sum of 24, start by listing the possible combinations.

Let's consider even numbers starting from 2 and progressively increase to satisfy the condition of four positive even numbers summing up to 24.

Here are the ways to add four positive even numbers to get a sum of 24:

2 + 2 + 2 + 18 = 24

2 + 2 + 4 + 16 = 24

2 + 2 + 6 + 14 = 24

2 + 2 + 8 + 12 = 24

2 + 4 + 4 + 14 = 24

2 + 4 + 6 + 12 = 24

2 + 4 + 8 + 10 = 24

2 + 6 + 6 + 10 = 24

4 + 4 + 4 + 12 = 24

4 + 4 + 6 + 10 = 24

4 + 6 + 6 + 8 = 24

There are a total of 11 ways to achieve this.