Question

Let the number of integers between 1 and 2021 with the property that the sum of its digits is 9 is p. Find p/2.

Answer 1

Given :  number of integers between 1 and 2021 with the property that the sum of its digits is 9  is p

To Find : p/2​

Solution:

1 and 2 Digit number  = 9 ,  18 , 27 , 36 , 45 , 54 , 63 , 72 , 81 , 90  hence 10 numbers

3 Digit numbers

Starting  with 1   Sum  108 , 117 , 126 , 135 , 144 , 153 , 162 , 171 , 180   hence 9

Starting  with 2   Sum 207 , 216 , 225 , 234 , 243 , 252 , 261 , 270    hence 8

and so on

Starting with 8   801 , 810  hence 2

Starting with 9    900  hence 1

4 Digit numbers

1008 to    1080     9 numbers

1107   to  1170    8 number

1800                   1 number

Then 2007   , 2016  

p = 10 +  2 ( 9 + 8 +  7 + 6 + 5 + 4 + 3 + 2 + 1)  + 2

p = 10 + 90 + 2

p = 102

p/2 = 51

Hence p/2 = 51

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