Sunday 6 April 2014

no computers - If 6 was 9, or 100 was 64, or M was N


         Now if a 6,
         Turned out to be 9,

         I don’ t mind,
         I don’ t mind   – Jimi Hendrix in If 6 was 9


Cool. Suppose a 100 turned out to be 64.


         I don’ t care,
         I don’ t care   – Jimi Hendrix in If 6 was 9


But, but Jimi, what if your computer program is bugged out and can’t tell if its bad self is coming (from octal) or going (to hex)?


          1008    =  6410
          10010  =  6416
          10016  =  6442


         Let it be,

         It ain’ t me   – Jimi Hendrix in If 6 was 9


You know, 1008 stands for the digits 100 in base 8, equaling the familiar 64 (in base 10), which itself shows as 6410.


         Dig    – Jimi Hendrix in If 6 was 9


So, that used 6 different digits — 0, 1, 2, 4, 6, 8 — a total of 26 times and bubbles down to...


         K  W  =  L X
         K X   =  L Y
         K Y   =  L Z
         ...where   K = 100,   L = 64,   W = 8,   X = 10,   Y = 16   and   Z = 42.


         I’ m gonna wave my freak flag high! – Jimi Hendrix in If 6 was 9




       Hold tight, hitch-hiker, check out where simpler ingredients can take you.




Just 4 different digits from 0 through 9, taken fewer than 43 times total, can really wig you out.


         M P   =  N Q     ( M > N   and   P < Q < R < S < T )
         M Q  =  N R
         M R  =  N S
         M S   =  N T


     Wild.   What M, N, P, Q, R, S and T could do that with the fewest digits total?


         Even a 43-digits-total solution or two would be worth posting.




         Wave on,
         Wave on . . .
         . . .’ Cause everybody knows what I’ m talking about
          – Jimi Hendrix in If 6 was 9 (vocal track) dailymotion



Answer



Well, I have a working set, it seems:



1011 (base 1) = 11 (base 2)
1011 (base 2) = 11 (base 10)

1011 (base 10) = 11 (base 1010)
1011 (base 1010) = 11 (base 1030302010)



using 4 digits (0,1,2 and 3) and the total number of times those numbers used is - 49 times (well, it was above the 43 limit...) and


assuming fractional bases are valid, here is another one:



22 (base 2.25) = 11 (base 5.5)
22 (base 5.5) = 11 (base 12)
22 (base 12) = 11 (base 25)
22 (base 25) = 11 (base 51 )




using 3 digits (1, 2 and 5) and the total number of times those numbers used is 33.


Here is another one:



111 (base 2) = 21 (base 3)
111 (base 3) = 21 (base 6)
111 (base 6) = 21 (base 21)
111 (base 21) = 21 (base 231)



using 4 digits (1, 2, 3 and 6) and the total number of times those numbers used is 32. Hope this satisfies @humn's requirements in all manners.



No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...