Challenging P6

Find the sum of the digits of the first 100 odd numbers.


First 100 odd numbers 1, 3, 5, ....., 199

Digits of first 100 numbers

   1 ,   3 ,   5 ,   7 ,   9 --> 25
 11 , 13 , 15 , 17 , 19 --> 25 + 1 x 5
 21 , 23 , 25 , 27 , 29 --> 25 + 2 x 5
...
 91 , 93 , 95 , 97 , 99 --> 25 + 9 x 5

101 , 103 , 105, 107 , 109 --> 25 + 1 x 5
111 , 113 , 115 , 117 , 119 --> 25 + 1 x 5 + 1 x 5
121 , 123 , 125 , 127 , 129 --> 25 + 1 x 5 + 2 x 5
....
191 , 193 , 195 , 197 , 199 --> 25 + 1 x 5 + 9 x 5

20 x 25 = 500

1 x 5 + 2 x 5 + .... + 9 x 5 = 5 x (1 + 2 + 9)
                                         = 5 x (1+9)/2 x 9
                                         = 225

225 x 2 = 450

10 x 1 x 5 = 50

500 + 450 + 50 = 1000

The sum of digits of the first 100 odd numbers is 1000.