September 2010 Brain Teaser Solution

When writing the whole numbers from 1 to 20, there are 12 1s (one in 1, 10, 12, 13, 14, 15, 16, 17, 18 and 19 and two in 11).  When writing the whole numbers from 1 to 1000, how many 1s will you write?

1- 99           20
100 - 199  120
200 - 299    20
300 - 399    20
400 - 499    20
500 - 599    20
600 - 699    20
700 - 799    20
800 - 899    20
900 - 999    20
1000              1

Total          301    

There are 12 1's from 1- 20

then 21, 31, 41, 51, 61, 71, 81, and 91

From 1 - 99, you will write a total of 20 ones

The same is true for 200 - 299, 300 - 399, 400 - 499, 500-599, 600 - 699, 700 - 799, 800 - 899, and 900-999. So from 200 - 999, there are a total of 160 ones (8 x 20)

From 100 - 199,

there are 20 ones in the second and/or third digit:

101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 131, 141, 151, 161, 171, 181, 191

plus all the ones that begin every number from 100 - 199 inclusive: 100