list of all combinations

Question

I have an electrical combination lock on my door. The combination is on two buttons. I know the combination, meaning I know which buttons and what order to push them to get the lock to open. I push button one, then two, then one, then two. Button one has a 3 and a 4 on it, button two has a 7 and a 8 on it. So if you wanted to memorize the combination, it would be 3737 or 4848 or 4738 etc. In other words the first (and third) number is either a 3 or 4, and the second (and forth) number is either a 7 or eight. What are all the possible numeric combinations to my lock

Answer 1

Reword the question:

Q:  "A dour-digit combination is composed of:  (3,4) then (7,8) then (3,4) then (7,8).  What are possibilities?

 

A:  Since the four digits are independent (and may be repeated), there are 2*2*2*2 =16 possibilities.  They are:

        digits       count in binary    Hexadecimal digit

       -------      ----------------      ------------------

     3 7 3 7            0 0 0 0                      0

     3 7 3 8            0 0 0 1                      1

     3 7 4 7            0 0 1 0                      2

     3 7 4 8            0 0 1 1                      3

     3 8 3 7            0 1 0 0                      4

     3 8 3 8            0 1 0 1                      5

     3 8 4 7            0 1 1 0                      6

     3 8 4 8            0 1 1 1                      7

     4 7 3 7            1 0 0 0                      8

     4 7 3 8            1 0 0 1                      9

     4 7 4 7            1 0 1 0                      A

     4 7 4 8            1 0 1 1                      B

     4 8 3 7            1 1 0 0                      C

     4 8 3 8            1 1 0 1                      D

     4 8 4 7            1 1 1 0                      E

     4 8 4 8            1 1 1 1                      F

 

Now, how easy would it be to memorize?:

               My combination is 9

 

                    9 is 1 0 0 1       (you must memorize the binary digits for the hexadecimal values)

                    9 is  4 7 3 8