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# How many numbers are there?

from 1 to 10000,

exclude numbers which have 4 or 9.

How many numbers are there ?

### 6 Answers

- JoeLv 55 years agoFavorite Answer
The number is 4096

The best way to think of this one is to progressively remove the uncounted numbers.

we start with 10000, and we know all 4000's and 9000's have to be removed.

Each 10000 is 10% of the total so we remove 20% of the numbers ...

down to 8000.

Now with the stuff left we have to remove all the 400's and 900's

that is also 20% that is 1600..etc , do that for the 10's and 1's and you end up with 4096

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

START 10000

remove thousands 2000 8000

remove hundreds 1600 6400

remove tens 1280 5120

remove ones 1024 4096

- Anonymous5 years ago
It's easier if you look at allowing leading zeros. That doesn't change the value of the number, but makes counting them easier.

Start with 4-digit numbers. Each digit has 8 possibilities, so there are 8^4 = 2^12 = 4096 numbers.

You have to toss out 0000 since that's too low. Then you add 10000 since that's 5 digits. You end up with the same number 4096.

4096 is the answer.

- NickLv 65 years ago
Numbers up to 9999 that don't have 4 or 9 = 8^4 = 4096

add 1 for 10000 which had neither:

4097 <----

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- Keith ALv 65 years ago
There are two options for the ten-thousand position, 1 and 0. That the zero just disappears doe not matter.

For the other four digits, eight options:

2 * 8^4, = 2^13 = 8192