Deceptively Simple Integer Problem

[chillfactor]

[b

Homework Equations

none

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Mark44]

You're forgetting to add 71, 72, 73, ...,76, 78, 79 and 171, 172, 173, ...,176, 178, 179

 

[morrowcosom]

Well you know that for the hundreds it does not appear once, since the problem does not go up to 700. As for the tens you get all the all the 70's (70 through 79) and all the 170's (170 through 179). As for the ones you get one every 10 digits (7, 17, 27...187, 197).


I do not get why the answer is 38 instead of 40. Like you said, there are 1 7 every 10 numbers, which gives you 20 7's, But if you add 70...79 and 170...179 together, you get 20 more 7's, which gives you a grand total of 40 7's.

 

[Mark44]

Well you know that for the hundreds it does not appear once, since the problem does not go up to 700. As for the tens you get all the all the 70's (70 through 79) and all the 170's (170 through 179). As for the ones you get one every 10 digits (7, 17, 27...187, 197).


I do not get why the answer is 38 instead of 40. Like you said, there are 1 7 every 10 numbers, which gives you 20 7's, But if you add 70...79 and 170...179 together, you get 20 more 7's, which gives you a grand total of 40 7's.

You counted two numbers twice: 77 and 177.

Every tenth number starting with 7: {7, 17, 27, 37, ..., 77, 87, ...,167, 177, 187, 197}
70's group: {70, 71, 72, ... , 76, 77, 78, 79}
170's group: {170, 171, 172, ... , 176, 177, 178, 179}