Question

An integer consists of 110 digits such that any 10 consecutive digits is different. What is the sum of all the digits!?

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Answer 1

Step-by-step explanation:

let the 10 consecutive digits be = x, x+1,x+2, x+3, x+4, x+5, x+6, x+7, x+8, x+9

By condition,

x+x+1+x+2+x+3+x+4+x+5+x+6+x+7+x+8+x+9 = 110

or, 10x = 110-45

or, 10x= 65

or, x = 65/10

or, x= 13/2

Now take out the value of rest of the consecutive digits by the adding the numbers with the value of x for example-

x+1 = 13/2 +1

= 15/2

hope this answer will help you ☺️

Answer 2

Step-by-step explanation:

Given :

An integer consists of 110 digits such that any consecutive 10 digits is different.

To Find :

What is the sum of all the digits

Solution:

Total digits = 100

any consecutive 10 digits is different.

Hence each set of 10 digits will be having all 10 digits from

0 to 9

Sum of 10 10 digits from 0 to 9 = 9 (10)/2 = 45

There are 110 Digits

Hence 110/10 = 11 such combination

so total sum = 45 * 11

= 495

sum of all the digits = 495