+0  
 
-1
122
3
avatar+272 

 

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

 Feb 3, 2021
 #1
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0

99 000 or less

 

5 choices for each digit  

            55 = 3125

 Feb 3, 2021
 #2
avatar+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
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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

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