How many numbers between 100 and 600 have a 7 for at least one of the digits?

Answer 1

There aren't going to be any 7's in the hundreds digit, so first we look at how many there will be in the ones digit.

Since there will be a 7 for every 10 numbers, and there are 501 numbers between 100 and 600 inclusive), we'll have floor(501 / 10) = 50 sevens in the ones digit.

For the tens digit, we'll encounter 10 sevens for every 100, from 70 to 79, and so we have floor(501 / 100) = 5 times we'll have 70 - 79 so that's 5 * 10 = 50 sevens in the tens digit.

However, we don't want to know how many sevens there are, we want to exclude overlaps. Thus we subtract every instance of 77 we see (overlap!), and we have floor(501 / 100) = 5 overlaps.

50 + 50 - 5 = 95, so a total of 95 numbers will have the digit 7 at least once.

Answer 2

Well, darling, let's break it down for you. Between 100 and 600, there are 500 numbers. Out of those, 100 have a 7 in the hundreds place, 100 have a 7 in the tens place, and 100 have a 7 in the units place. But hold your horses, some numbers have 7 in more than one place, so you gotta subtract those duplicates. So, in total, you've got 271 numbers with at least one 7 in them.

Answer 3

Oh, dude, let me break it down for you. So, we're looking for numbers between 100 and 600 that have a 7 in them, right? Well, there are 9 numbers that have a 7 in the hundreds place (like 700, 701, etc.) and 90 numbers that have a 7 in the tens or units place (like 107, 217, 327... you get the idea). So, in total, there are 99 numbers between 100 and 600 that have a 7 in at least one of the digits.

Answer 4

Oh, what a happy little question! Let's see, we have numbers from 100 to 599, so that's 500 numbers in total. To find out how many have a 7 in them, we can count the numbers that don't have a 7 and subtract that from the total. If a number doesn't have a 7, it must have digits 1-6 or 0 in each place, so there are 6 choices for each place. That means there are 666 = 216 numbers without a 7. So, 500 total numbers minus 216 numbers without a 7 gives us 284 numbers that do have a 7 in them.