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avatar+146 

My three digit code is 023. Reckha can't choose a code that is the same as mine in two or more of the three digit positions, nor that is the same as mines except for switching the positions of two digits (so 320 and 203, for example, are forbidden, but 302 is fine). Reckha can otherwise choose any three-digit code where each digit is in the set {0, 1, 2, ..., 9}. How many codes are available for Reckha?

 Dec 8, 2018
 #1
avatar+4424 
+1

it's probably easiest to just list out the forbidden codes

 

023 - narrators code

 

02x

0x3

x23

where x is a digit from 0-9, there are 10 each of these for a total of 30

 

203

302

032

 

So there are a total of 34 forbidden codes

 

There are a total of 103 = 1000 codes

 

1000 - 34 = 966 available codes

 Dec 8, 2018

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