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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 mine 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?

 Jun 17, 2021
 #1
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plz help

 Jun 17, 2021
 #2
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NOT allowed would be   023   (not allowed bcause all 3 positions are the same as yours)  

               also not allowed: 032   203   320   as only two numbers have switched places

ALSO  NOT allowed would be   x23  (nine codes ...we already counted the o23)     0x3   (nine codes....we counted 023)   and  02x    (nine codes again) codes)

      

total codes POSSIBE    10 x 10 x 10 = 1000

   minus the not allowed codes above = 1000 -1-1-1-1-9-9-9 =___________ possible codes    (I think!)

 Jun 18, 2021
 #3
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thanks for the help! 

Guest Jun 18, 2021

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