what is the sum of the digits of the decimal form of the number represented by brain teaser 2

The Sum of Digits in Brain Teaser Numbers: Unraveling the Mystery

Brain teasers are a delightful way to challenge our minds and test our problem-solving skills. One such brain teaser that has been making rounds online is the puzzle of finding the sum of the digits of the decimal form of the number represented by using certain digits. In this article, we'll dive into the intricacies of this puzzle and explore the solution.

The Puzzle: What is the Sum of the Digits?

The problem statement reads: 'What is the sum of all the 4-digit numbers formed by digits 2,3,4,5?' At first glance, it may seem like a daunting task, but let's break it down to understand what we're dealing with.

As mentioned in the puzzle, there are 24 possible combinations of these four digits. What this means is that each digit will appear six times in the decimal form of the number represented by these digits. The numbers will be of the form 2354 or 3425 and so on.

To calculate the total number of combinations, we can use the formula for permutations: 4*3*2*1 = 24. This tells us that there are indeed 24 unique four-digit numbers formed using these digits.

The Solution

Now that we have an understanding of what's at play, let's tackle the problem head-on. We need to calculate the sum of all the digits in each combination and then add them up to find the total sum.

One way to approach this is to create a list of all the possible combinations and then calculate their digit sums individually. However, there's an easier way to solve this puzzle using mathematical reasoning.

Since all the digits are equivalent, we can simply calculate the average digit value and multiply it by 24 (the number of combinations). This gives us:

(2 + 3 + 4 + 5) / 4 * 24

= 14 / 4 * 24

= 3.5 * 24

= 84

So, the sum of all the digits in the decimal form of the numbers represented by these digits is 84.

In this article, we've explored the puzzle of finding the sum of the digits of the decimal form of the number represented by using certain digits. By understanding the permutations and combinations involved, we can break down the problem into manageable chunks and arrive at a solution. The key takeaway is that when all the digits are equivalent, we can calculate the average digit value and multiply it by the total number of combinations to find the sum.

We hope this article has provided valuable insights into solving this brain teaser. If you have any questions or would like to share your own puzzle-solving experiences, please feel free to comment below!

What is the sum of the digits of the decimal form of the number represented by brain teaser 2