Two Wrongs Sometimes Equal a Right

two_wrongs.ijs

NB. Nicholas Paul
NB. 9 Dec 2016

NB. Suppose every letter below represents a distinct positive
NB.   integer, non of which are zero. What is a possible value
NB.   for each letter?
NB.
NB.     W R O N G
NB.   + W R O N G
NB.   -----------
NB.     R I G H T


NB. Table of all permutations
NB. For example,
NB.    tap 3
NB. 0 1 2
NB. 0 2 1
NB. 1 0 2
NB. 1 2 0
NB. 2 0 1
NB. 2 1 0

tap=: i.@! A. i.



NB. Test function
NB. Return true if 2* the first 5 numbers (w,r,o,n,g) is
NB.   equal to the 1,5,4,6,7 (r,i,g,h,t) number
NB.
NB. ((  (2&*)            Multiply By 2
NB.  @: (10&#.)          List to num: 1 2 3 => 123
NB.  @: (5&{.)           Let w,r,o,n,g be the first 5 numbers
NB. ) = (              Test if equal to ...
NB.     (10&#.)          List to num: 1 2 3 => 123
NB.  @: (1 5 4 6 7 &{)   Indices for r,i,g,h,t
NB. )) "1                Rank 1 so we can apply it to lists in a table
NB.

two_wrongs =: (((2&*) @: (10&#.)@:(5&{.)) = ((10&#.) @: (1 5 4 6 7 &{))) "1



NB. Filter using the test function on all combinations
NB. 1 + (tap 9) generates permutations of the list (1 2 3 4 5 6 7 8 9)
NB. two_wrongs # ] filters all lists that make the statement true
NB. 8 {."1 takes the first 8 elements of each row in the list

res =: 8 {."1 ( two_wrongs # ] ) 1 + (tap 9)

NB. Pretty Print

,./ ((< & ((5&{.,:5&{.)) ,: (<&(1 5 4 6 7 &{)))) "1 [ res