Sum of all the Numbers of any number of Digits with Tricks

Sum of digits of 2 or 3 digits commonly ask in the aptitude section. This questions we can do without going for large calculations. With a simple formula we can do it in a single step. Please focus on how to solve it with minimum time. All we should try to minimize time and complexity to solve any problem.


-> Find out four digits distinct numbers sum which is formed by using 2,7,9,5,1 digits ?

Ans  Four digits numbers can be written as

4 digit number=1000a+100b+10c+d

Number formed with these digits with repetition = ⁵P₄   

=120

As all digits contributes equally to hundred's, ten's and one's digit. So

-> Contribution to Thousand's Digit = 120/5 = 24

-> Contribution to Hundred's Digit = 120/5 = 24

-> Contribution to Ten's Digit = 120/5 = 24

-> Contribution to One's Digit = 120/5 = 24

Remember all digits r non-zero means 2,7,9,5,1 does n't consists 0.

If it consists zero then slightly change in contribution to Thousand's digit.

That's 120/4 = 30

Note : 0 not contribute to first digit of any number or starting digit of number

Can you assume 4 digit number as 0234 ? Really not



Now Sum of All 4 Digits Numbers = 1000 * 24 * (2+7+9+5+1) + 100 * 24 * (2+7+9+5+1) + 10 * 24 * (2+7+9+5+1) + 1 * 24 * (2+7+9+5+1).

=  24000 * 24 + 2400 * 24 + 240 * 24 + 24 * 24

= 24 (24000+2400+240+24)

= 24 (26664)

= 639936

Or simply  (n)! (sum of digits) X (1111 upto n times) 


In this manner we can do the sum of any digit number. Remember digits r not repeated in this Case.



Digital Sum of Any number = sum of the digits of particular number

for ex -  23109

digital sum = 2+3+1+0+9 = 15 = 1+5 = 6



Verfiy multiplication of a number

Suppose we have two numbers

34 X 45 = 1234

Now we want to check if this is correct multiplication

(3+4) * (4+5) = (1+2+3+4)

7 * 9 = 10

63 =10

(6+3) = 10

9=10 . InCorrect Multiplication


-> 12 * 12 =144

(1+2) * (1+2) = 4+4+1

3*3 = 9

9 = 9 , Correct Multiplication


Some questions can do only with this technique as


find value of A+B ?

A45092233B * 10 = 230000010

Don't count 9 or sum 9 in finding digital sum.

A+B+1=6

A+B=5



Unit Digit of a number


->34 * 33 * 1000 * 787888 * 9999991222

Unit digit = ?

-> As above multiplication consists 1000 or a number ending with zero . So result contains zero at its end.

Unit's digit =0

Same 5 * 2 =10

5 * 4 =20

5 * 8 =40

5 * 6 =20

Any even number multiplied with Any number ends with unit's digit 5 = Unit's digit 0

->34 * 77 * 99 * 11111111 * 345 * 1002

As 5 * 2 =10

Therefore unit's digit = 0


->Unit's digit of any number ending with 1

34599999999991222331^{889988388838828}

As number end with digit 1

Unit's digit of above number = 1


-> Unit digit of any multiplication except above case (0 or 5)

89 * 877 * 76 = 9 * 7 * 6 = 63 * 6 = 3 * 6 = 18

So 8




Last Two Digits of Any Number


->Last two digit of 76ⁿ is 76

-> Last two digit from multiplication

12342 * 998 * 1007 = 42 * 98 * 07 = 28812 = 12

-> Last two digits of number end up with 1.

-> 12341³⁵²⁹ = Last two digits is multiplication of unit's digit of exponent and ten's digit of number.

In this case  9 * 4 = 36  and unit's digit 1

= So last two digit is 61


-> Last two digits of any even number

346⁹⁶= Last two digits is break the number into two parts even and odd dividing by 2.

(173)⁹⁶*2⁹⁶=

First make 173 into number end with 1

last digit of 173 is 3 and 3 raise to power 4 = 81.

So 173^4*24=(173⁴)²⁴=

Find last 2 digits of 173 raise to the power 4 becoz we need to find only last two digits.

73 raise to power 4 = ?


-> 73 raise to power 2 * 73 raise to power 2

-> 73 raise to power 2 is

73   -27   (The Method is Below to Calculate Square)
73   -27
------------
46 729

46 + 7 29

5329 is Ans

So 29 * 29 = 29(30-1) =870-29=841

Last two digit of 173⁴ is 41

Therefore 41²⁴*2²⁴= (61) * 2^10*2*2⁴= 16 * 76 * 16 =61 * 76 * 16 =  76

Last two digits is 76.



How to find square of a number easily ?

As we know we can express a number into sum of odd numbers.

1*1 = 1
2*2 = 1 + 3
3*3 = 1 + 3 + 5
4*4= 16 = 1 + 3 + 5 + 7
5*5 = 25 = 1 + 3 + 5 + 7 +.....................(2n-1)

Hence we can say that

26 * 26 = 25 * 25 + 26th Odd Number

Or

Square of number less than 50

= 43²=

Find difference from 50 = 50-43 = 7

Substract this difference from 25 = 25 - 7 = 18

Square first difference 7 * 7 =49

Required No. is  1849


Square of a number above 50

= 57²=

Add last digit to 25 = 25+7=32

Square last digit 7*7=49

Required Number is 3249


Square of any number closer to 100 or multiplication of numbers closer to 100.

By Using this Method We can solve complicated problems with ease. Thanks