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# How many counting numbers less than 100000 have only even digits?

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122
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+272

How many counting numbers less than 100000 have only even digits?

Feb 3, 2021

### 3+0 Answers

#1
0

99 000 or less

5 choices for each digit

55 = 3125

Feb 3, 2021
#2
+1764
0

Hi Guest!

You're really close, but the first digit only has 4 options since it can't be 0.

4*5*5*5*5 = 2500

=^._.^=

Edit:

I've made a dumb error... >:(((

So I forgot that numbers exist that aren't 5 digit.-.-

So please ignore that previous response.

As for why the 2 guests have gotten different answers is because 0 is also counted using the method: 5^5 = 3125, so you just have to subtract 1.

Nice job to our guests for solving the problem... I'm quite sad that I've made such a dumb mistake.

=^._.^=

catmg  Feb 3, 2021
edited by catmg  Feb 4, 2021
#3
0

There are: 4 between 1 and 10

20 between 10 and 100

4 x 5 x 5 =100 between 100 and 1,000

4 x 5 x 5 x 5=500 between 1,000 and 10,000

4 x 5 x 5 x 5 x 5 =2,500 between 10,000 and 100,000

Grand Total =[4 + 20 + 100 + 500 + 2,500] ==3, 124 integers with EVEN digits.

Feb 4, 2021