NB. puzzle: substitute the digits 0-9 for the the letters
NB. to form a magic square of sum 99
NB. (published puzzle hinted that y is 8 should you try it with pen
and paper)
_4 [\ ;:'ph h ne th na tc he e pn nx y pp a pt pv nc'
┌──┬──┬──┬──┐
│ph│h │ne│th│
├──┼──┼──┼──┤
│na│tc│he│e │
├──┼──┼──┼──┤
│pn│nx│y │pp│
├──┼──┼──┼──┤
│a │pt│pv│nc│
└──┴──┴──┴──┘
NB. a solution with Engine: j902/j64avx2/linux Beta-j:
commercial/2020-10-29T16:04:59
NB. !10 is small enough to try all permutations.
NB. method: select solutions from all literal puzzle substitutions
A=:'ph h ne th na tc he e pn nx y pp a pt pv nc'
S=: ' ' ([ ,~ (-.~ ~.)) A NB. 'phnetacxyv ' the set of puzzle
character with space at index 10
NB. I is the puzzle converted to indices,
I=: S i. A
NB. w computes to 1 iff all rows, columns, and diagonals sum to 99
w=: (0 -.@e. 99 = +/ , +/"1 , +/@:((<0 1)&|:) , +/@:((<0
1)&|:)@:|:)@:(_4 [\ 0&".)
NB. P is a table of all permutations of the digits, followed by the
space character
P=:' ' ,.~ ({~ (A.&i.~ !)@:#) Num_j_
NB. literal table J are all substitutions
J=:I {"1 P
NB. for example here are the head and tail rows
({. ,: {:) J
01 1 23 41 25 46 13 3 02 27 8 00 5 04 09 26
98 8 76 58 74 53 86 6 97 72 1 99 4 95 90 73
NB. filter solutions
SOLUTIONS=: (#~ w"1) J
$ SOLUTIONS
1 43
datatype SOLUTIONS
literal
A, SOLUTIONS
ph h ne th na tc he e pn nx y pp a pt pv nc
21 1 46 31 47 30 16 6 24 45 8 22 7 23 29 40
(_4 ]\ ".)"1 SOLUTIONS
21 1 46 31
47 30 16 6
24 45 8 22
7 23 29 40
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