Question

how many integers between 100 and 400 contain the digit 2

Answer 1

Between 100 and 400 means from 101 to 399.
Think of different intervals:
101 to 199
200 to 300
301 to 399

Answer 2

The easy interval is from 200 to 300 in which all integers from 200 to 299 have a 2.
That is 100 integers with a 2.

Now think of the interval 101 to 199.
From 120 to 129, every integer has a 2. That is 10 2's.

Also, in every group of 10, there is one 2.
100 to 119, there is one 2
120 to 129 there are 10 2's
130 to 140 there is one 2
etc.

Then the interval 301 to 399 is the same as the interval 101 to 199.

Answer 3

I counted to be 138. not sure though. This problem is a little bit tougher than I originally thought

Answer 4

I got 136.

Answer 5

I got the same thing 136 and I did it the long way

Answer 6

is there an easy way to do it?

Answer 7

shouldn't there be 19 numbers from 100-199 containing the digit 2?
same thing from 300-399?
and from 200-299 obviously has 100

so 19 + 19 + 100 = 138?

Answer 8

102, 112, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 132, 142, 152, 162, 172, 182, 192

Answer 9

100 + 2(1*1*10) - 1 + 2(1*1*10) - 1 = 138

Answer 10

I see where I missed counting one in the 101-199 counting, which then turned to two less when including the 300-399. Yes, 138 makes sense. Thanks.