Friday, July 22, 2016

Hello, I need help, I cant remember my cell phone pin i set last night. It is a four digit number using numbers 0-9, the only thing i remember is...

Hello!


There are pins at all. Denote the set of pins that contain no 1's as and that contain no 3's as


We'll use the formula which is true for any finite sets, particularly for and  ( means the number of elements).


The set of pins that contain 1 AND contain 3 is the complement of those which don't contain 1 OR don't contain 3, i.e. The number of pins in this set is By the above formula it is



It is clear that (any number except 1 at any of 4 positions), and is the same. is the number of pins that don't contain 1 AND don't contain 3, there are of those (any number except 1 and 3 at any position).


So the answer is


There are too many variants to try, it is necessary to recall the pin. Try the following trick: imagine that you want to set a new pin, what could it be?

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