One simple way, not optimal, but not terribly bad, I think,
for burglars anyway ...
NB. 4 burg 5
burg=: 4 : 0
B=. x#y
L=. ''
for_i. i.y^x do.
p=. B#:i
if. -.p +./@E. L do. L=. L,p end.
end.
L
)
4 %~# 4 burg 5
166
$ ((4#5)#:i.5^4) (+/@E."1 _) 4 burg 5
625
0 e. ((4#5)#:i.5^4) (+/@E."1 _) 4 burg 5
0
--- On Tue, 6/24/08, Devon McCormick <[EMAIL PROTECTED]> wrote:
> Dan - I solved a similar problem a number of years ago ...
> that I came up with a 101-digit "universal" answering machine
#2 burg 10
110
$ ((2#10)#:i.10^2) (+/@E."1 _) 2 burg 10
100
0 e. ((2#10)#:i.10^2) (+/@E."1 _) 2 burg 10
0
--- On Tue, 6/24/08, Dan Bron <[EMAIL PROTECTED]> wrote:
> For convenience's sake, some cars allow you to unlock
> their doors with a numeric code rather than a key. The
> code is entered on a buttonpad on the door. Your mission,
> should you choose to accept it, is to become an efficient
> burglar of such cars. I'll start you off with some
> hints. Most cars have two glaring security flaws:
>
> (A) Unlike, for example, a computer keyboard or cell
> phone, there is
> no "enter" or "send" key. If
> you press the right 4 buttons in the
> right sequence, the car door unlocks.
> Importantly, the lock
> ignores everything before and after the right
> sequence is pressed.
>
> (B) You get as many chances as you want (you can
> press as many incorrect
> buttons as you like, with no ill consequences).
>
> Let's examine a concrete example. The following hold
> for most such locks:
>
> (C) The unlock code consists of 4 button-presses.
>
> (D) Though it appears there are 10 buttons, there are
> really
> only 5; each button merely carries two labels. So
> there's no
> difference between (eg) pressing "1" or
> "2":
>
> [1 | 2] [3 | 4] [5 | 6] [7 | 8] [9 | 0]
>
> So, if the buttons are labeled A B C D E respectively, and
> the unlock code is BCBC, then ABCBCC will open the door, as
> will DDDDDBCBCDDDDD, etc.
>
> Theoretically, there is some minimal length sequence which
> contains all possible codes (sub-sequences of 4 button
> pushes). Your job is to construct a J program to find this
> sequence (given the set of all buttons and the length of the
> unlock code).
>
> Put another way, write a dyadic J verb "burgle"
> whose output satisfies the following criteria: with the
> five buttons A B C D E and the unlock code key (with
> 4=#key ) then your sequence is defined by sequence =: 4
> burgle 'ABCDE' and key e. 4 ]\ sequence with
> #sequence minimized. Remember your dyad must be general
> enough to unlock a door with any number of buttons (given
> as the list y ) and an unlock sequence of any length
> (given as the integer x ).
>
> -Dan
>
> PS: I stole this idea from
> http://www.everything2.com/index.pl?node_id=1520430 where
> the correct answer is given (for the specific case of 4=x
> and 5=#y ) in addition to pointers to the theory
> underlying its derivation. Try to solve the puzzle first
> before visiting the link.
>
> PPS: Here's a picture of a car buttonpad:
>
>
> http://bp3.blogger.com/_AKM4HWd7eMo/RwaWHOmXQmI/AAAAAAAAAAc/WE7U88UruSI/S760/keyless_entry.jpg
>
>
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