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## Comment on

Listing and Counting## Can you pl explain this - "In

I am confused by the solution.

1) I don't understand the conclusion 'all digits occur the same number of times'

2) is there a different way altogether to solve it, for example if were asked to count the number of zeros, this approach wont work right?

## Question link: http:/

Question link: http://greprepclub.com/forum/gre-math-challenge-306.html

1) If we focus on the UNITS digits as we count to 300, we get a units digit of 1 every 10 numbers. So, 1/10 of the 300 numbers will have 1 in the units digit place. This gives us 30 1's so far.

If we focus on the TENS digits as we count to 300, we get a 1 in the TENS location 10 times out of every 100 numbers (e.g., 210, 211, 212, 213..., 219). So, 1/10 of the 300 numbers will have 1 in the TENS digit place. This gives us another 30 1's.

Finally, the numbers from 100 to 199 have a 1 in the HUNDREDS position. So, there are another 100 1's here.

TOTAL = 30 + 30 + 100 = 160

2) We could modify this technique to make it work for counting 0's.

## Thank you.

Can you explain the solution in the case we had to find number of zeros used from 1 to 300.

According your above method I got - 30 + 9+ 9 + 1 = 49..

## You bet.

You bet.

NEW question: In writing all of the integers from 1 to 300, how many times is the digit 0 used?

0's IN THE UNITS POSITION

We get a 0 in the UNITS position once every 10 values: 10, 20, 30, 40, . . . 280, 290, and 300

In other words, 1/10 of the 300 numbers from 1 to 300 have a 0 in the UNITS position.

1/10 of 300 = 30, so we have 30 zeros so far

0's IN THE TENS POSITION

We get a 0 in the UNITS position in the following formats:

10-

20-

30-

NOTE: the "-" represents a units digit.

For the first case of 10-, the last (units) digit can be 0, 1, 2, 3, 4, ... 9. So, there are 10 zeros used (in the TENS position) in numbers in the 10- format.

Likewise, there are 10 zeros used (in the TENS position) in numbers in the 20- format.

Finally, there's only 1 zero used (in the TENS position) in the 30- format (300).

So, the TOTAL number of 0's used = 30 + 10 + 10 + 1 = 51 (just like you have!)

## For the second GRE Prep

I would have thought: 2 slots

First slot: 6 options

Second slot: 4 options

I don't want to double count AZ and ZA, so I divide my total of 24 by 2-factorial.

Is this not a combinations problem?

## Hi aseiden,

Hi aseiden,

Question link: http://greprepclub.com/forum/gre-math-challenge-117-on-elm-street-there-...

When you're breaking the task into stages (aka slots), you need to be clear what you're actually doing during that stage. For example, what do you mean by "Second slot: 4 options"?

If you state what you're doing in each of those stages, you'll see that there is no duplication. So, we need not divide our answer by 2.

To see what I mean, check out my new post: http://greprepclub.com/forum/gre-math-challenge-117-on-elm-street-there-...

## Please, regarding the

Am i right?

## Actually, 333 and 777 meet

Actually, 333 and 777 meet the condition of using only 3's and 7's

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