Thanks, David
Why these singletons and pairs of letters?
It looks as if some permutation of the 4x4 square of letter groups might
form words across and down. Then again, perhaps not, given pv and nx
and that there are only 3 solo (semi)vowels!
Mike
On 01/11/2020 17:17, David Lambert wrote:
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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