# WHAT IS THE SUM OF ALL THE THREE DIGIT NUMBERS FORMED FROM 1 3 4 ? (without repetition)

## About the topic "What is the sum of all the three digit numbers formed from 1 3 4?"

"What is the sum of all the three digit numbers formed from 1 3 4 ?" is a difficult problem having had by the students who study math to get prepared for competitive exams.

For some students, getting answer for the questions like "Find the sum of all 3 digit numbers formed using 1 3 4" is never being easy and always it is a challenging one.

Once we know the concept and method of solving, solving the above problem will not be a challenging one.

## List of numbers formed using the digits 1, 3, 4 without repetition

Since we are going to form three digit numbers, let us have three blanks.

____     ____     ____

The first blank (hundred's place) has three options from the given three digits.

They are 1, 3, 4

If one of the three digits (1, 3, 4) is filled in the first blank, two  digits will be remaining.

So, the second place has two options and it can be filled by one of the two digits.

After having filled the second blank, only one digit  will be remaining.

So, the third place has one option and it can be filled by the remaining one digit.

The above explained stuff can be written as

3x2x1 = 6

Therefore the number of three digit numbers formed from  1, 3, 4   is  6.

They are

134

143

314

341

413

431

Is it possible to write all the six numbers and find sum of them in exam as done above?

Then, is there any shortcut?

Yes. To know the shortcut, come to know the value of "K" using the formula given below.

Here, students may have question.

That is, what do we do with "K" to get answer for the question "What is the sum of all the three digit numbers formed from 1 3 4 ?"

## Concept - Value of "K"

What does "K" do if one of the digits is "zero"?

1. Each one of the non-zero digits will come "K" times at the first      place (hundred's place, if it is three digit number).

2. The digit "0" will come "K" times at the second place. The remaining blanks at the second place will be shared equally by the non-zero digits.

3. The same process which is explained above for the second place will be applied for the third place.

What does "K" do if none of the digits is "zero"?

Each one of the non-zero digits will come "K" times at the first place, second place and third place.

## How is the above concept applied in our problem?

In our problem, we have

K = 6/3

K = 2

In our problem we get  K = 2

In the given three digits, none of the digits is "0".

So, each one of the given three digits (1, 3, 4) will come at the hundred's place,ten's place and unit's place 2 ( = K ) times in the 6 numbers formed using 1, 3, 4  (Please see the 6 numbers above).

## Sum of numbers at the first, second and third places

To get answer for the question "What is the sum of all the three digit numbers formed from 1 3 4 ?", we have to find the sum of all numbers at first, second and third places.

Let us find the sum of numbers at the first place (hundred's place).

In the 6 numbers formed, we have each one of the digits (1, 3, 4) two times at the first place, second place and third place.

Sum of the numbers at the first place (100's place)

=  2(1+3+4)  =  2x8  =  16

Sum of the numbers at the second place (10's place)

=  2(1+3+4)  =  2x8  =  16

Sum of the numbers at the third place (1's place)

=  2(1+3+4)  =  2x8  =  16

## What is the sum of all the three digit numbers formed from 1 3 4 ?

Explanation for the above calculation:

16 is the sum of numbers at hundred's place. So 16 is multiplied 100.

16 is the sum of numbers at ten's place. So 16 is multiplied 10.

16 is the sum of numbers at unit's place. So 16 is multiplied 1.

The method explained above is not only applicable to get answer for the questions like "What is the sum of all the three digit numbers formed from 1 3 4 ?" This same method can be applied to find sum of all 3 digit numbers formed using any three digits in which none of the digits is zero.

When students have the questions like " What is the sum of all the three digit numbers formed from 1 3 4 ?", in competitive exams, they are stumbling a lot to solve. If we know the way of solving, getting answer for the questions like " What is the sum of all the three digit numbers formed from 1 3 4 ?" is not a difficult task.

We hope, after having seen the methods and steps explained above, students will not find it difficult to answer the questions like "What is the sum of all the three digit numbers formed from 1 3 4 ?".