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?

Guest Jun 17, 2021

#2**+1 **

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!)

ElectricPavlov Jun 18, 2021