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Twisted TALES (Posted on 2010-03-20) Difficulty: 3 of 5
The letters of TALES have been added to the grid to form six words, one being a lingual import into English.

L E A S T
S L A T E
S T A L E
S T E A L
T A E L S
T A L E S

Assign a base 10 digit to each of the letters in the grid to create an alphametic so that each row but one forms a 5-digit prime number.

This situation can occur in three ways, and logic should prevail.

See The Solution Submitted by brianjn    
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re(2): computer solution | Comment 6 of 7 |
(In reply to re: computer solution by Dej Mar)

    5   dim Used(9),Pv(12)
   10   for L=0 to 9
   15    Used(L)=1
   20    for S=0 to 9
   30     if Used(S)=0 then
   35      :Used(S)=1
   40      :for T=0 to 9
   42        :if Used(T)=0 then
   44          :Used(T)=1
   50      :for A=0 to 9
   52        :if Used(A)=0 then
   54          :Used(A)=1
   56      :for E=0 to 9
   60        :if Used(E)=0 then
   70          :Used(E)=1
   75          :Least=L*10000+E*1000+A*100+S*10+T
   76          :Slate=S*10000+L*1000+A*100+T*10+E
   77          :Stale=S*10000+T*1000+A*100+L*10+E
   78          :Steal=S*10000+T*1000+E*100+A*10+L
   79          :Taels=T*10000+A*1000+E*100+L*10+S
   80          :Tales=T*10000+A*1000+L*100+E*10+S
   81          :Leats=L*10000+E*1000+A*100+T*10+S
   82          :Salet=S*10000+A*1000+L*100+E*10+T
   83          :Setal=S*10000+E*1000+T*100+A*10+L
   84          :Stela=S*10000+T*1000+E*100+L*10+A
   85          :Teals=T*10000+E*1000+A*100+L*10+S
   86          :Tesla=T*10000+E*1000+S*100+L*10+A
  181          :Prmcnt=0:for I=1 to 12:Pv(I)=0:next
  182          :if prmdiv(Least)=Least then Prmcnt=Prmcnt+1:Pv(1)=1:endif
  183          :if prmdiv(Slate)=Slate then Prmcnt=Prmcnt+1:Pv(2)=1:endif
  184          :if prmdiv(Stale)=Stale then Prmcnt=Prmcnt+1:Pv(3)=1:endif
  185          :if prmdiv(Steal)=Steal then Prmcnt=Prmcnt+1:Pv(4)=1:endif
  186          :if prmdiv(Taels)=Taels then Prmcnt=Prmcnt+1:Pv(5)=1:endif
  187          :if prmdiv(Tales)=Tales then Prmcnt=Prmcnt+1:Pv(6)=1:endif
  188          :if prmdiv(Leats)=Leats then Prmcnt=Prmcnt+1:Pv(7)=1:endif
  189          :if prmdiv(Salet)=Salet then Prmcnt=Prmcnt+1:Pv(8)=1:endif
  190          :if prmdiv(Setal)=Setal then Prmcnt=Prmcnt+1:Pv(9)=1:endif
  191          :if prmdiv(Stela)=Stela then Prmcnt=Prmcnt+1:Pv(10)=1:endif
  192          :if prmdiv(Teals)=Teals then Prmcnt=Prmcnt+1:Pv(11)=1:endif
  193          :if prmdiv(Tesla)=Tesla then Prmcnt=Prmcnt+1:Pv(12)=1:endif
  200          :if Prmcnt>=Max then
  205            :if Prmcnt>Max then Sct=0:Max=Prmcnt:endif
  210            :print:print "least";Least;Pv(1):print "slate";Slate;Pv(2)
  211            :print "stale";Stale;Pv(3):print "steal";Steal;Pv(4):print "taels";Taels;Pv(5)
  215            :print "tales";Tales;Pv(6)
  220            :print "leats";Leats;Pv(7):print "salet";Salet;Pv(8):print "setal";Setal;Pv(9)
  221            :print "stela";Stela;Pv(10):print "teals";Teals;Pv(11)
  225            :print "tesla";Tesla;Pv(12)
  280            :print Prmcnt:Sct=Sct+1
  290          :endif
  291          :Used(E)=0
  292        :endif
  293      :next E
  294          :Used(A)=0
  295        :endif
  296      :next A
  297          :Used(T)=0
  298        :endif
  299      :next T
  300      :Used(S)=0
  310     :endif
  320    next S
  325    Used(L)=0
  330   next L
  350   print Sct
finds two solutions with 8 primes apiece:
least 73019  1
slate 17093  1
stale 19073  1
steal 19307  0
taels 90371  1
tales 90731  1
leats 73091  1
salet 10739  1
setal 13907  1
stela 19370  0
teals 93071  0
tesla 93170  0
 8
least 73891  0
slate 97813  1
stale 91873  1
steal 91387  1
taels 18379  1
tales 18739  0
leats 73819  1
salet 98731  1
setal 93187  1
stela 91378  0
teals 13879  1
tesla 13978  0
 8
 

And there are 14 solutions with 7 primes(leading zeros included, but with the leading zeros not shown on the printout):

least 7139  0 
slate 30197  1
stale 39107  1
steal 39710  0
taels 91703  1
tales 91073  0
leats 7193  1
salet 31079  1
setal 37910  0
stela 39701  0
teals 97103  1
tesla 97301  1
 7
least 15439  1 
slate 31495  0
stale 39415  0
steal 39541  1
taels 94513  1
tales 94153  1
leats 15493  1
salet 34159  1
setal 35941  0
stela 39514  0
teals 95413  1
tesla 95314  0
 7
least 18379  1 
slate 71398  0
stale 79318  0
steal 79831  0
taels 93817  0
tales 93187  1
leats 18397  1
salet 73189  1
setal 78931  0
stela 79813  1
teals 98317  1
tesla 98713  1
 7
least 13795  0 
slate 91753  1
stale 95713  1
steal 95371  0
taels 57319  0
tales 57139  1
leats 13759  1
salet 97135  0
setal 93571  0
stela 95317  1
teals 53719  1
tesla 53917  1
 7
least 18397  1 
slate 91378  0
stale 97318  0
steal 97831  0
taels 73819  1
tales 73189  1
leats 18379  1
salet 93187  1
setal 98731  1
stela 97813  1
teals 78319  0
tesla 78913  0
 7
least 27935  0 
slate 32957  1
stale 35927  0
steal 35792  0
taels 59723  1
tales 59273  1
leats 27953  1
salet 39275  0
setal 37592  0
stela 35729  1
teals 57923  1
tesla 57329  1
 7
least 29437  1 
slate 32479  1
stale 37429  0
steal 37942  0
taels 74923  1
tales 74293  1
leats 29473  1
salet 34297  1
setal 39742  0
stela 37924  0
teals 79423  1
tesla 79324  0
 7
least 21839  1 
slate 32891  0
stale 39821  1
steal 39182  0
taels 98123  1
tales 98213  1
leats 21893  1
salet 38219  1
setal 31982  0
stela 39128  0
teals 91823  1
tesla 91328  0
 7
least 32917  1 
slate 13972  0
stale 17932  0
steal 17293  1
taels 79231  1
tales 79321  0
leats 32971  1
salet 19327  0
setal 12793  0
stela 17239  1
teals 72931  1
tesla 72139  1
 7
least 41539  1 
slate 34591  1
stale 39541  1
steal 39154  0
taels 95143  1
tales 95413  1
leats 41593  1
salet 35419  1
setal 31954  0
stela 39145  0
teals 91543  0
tesla 91345  0
 7
least 51439  1 
slate 35491  1
stale 39451  1
steal 39145  0
taels 94153  1
tales 94513  1
leats 51493  0
salet 34519  1
setal 31945  0
stela 39154  0
teals 91453  1
tesla 91354  0
 7
least 53791  1 
slate 95713  1
stale 91753  1
steal 91375  0
taels 17359  1
tales 17539  1
leats 53719  1
salet 97531  0
setal 93175  0
stela 91357  0
teals 13759  1
tesla 13957  0
 7
least 53194  0 
slate 95143  1
stale 94153  1
steal 94315  0
taels 41359  0
tales 41539  1
leats 53149  1
salet 91534  0
setal 93415  0
stela 94351  1
teals 43159  1
tesla 43951  1
 7
least 79813  1 
slate 17839  1
stale 13879  1
steal 13987  0
taels 38971  1
tales 38791  1
leats 79831  0
salet 18793  1
setal 19387  1
stela 13978  0
teals 39871  0
tesla 39178  0
 7

Edited on March 21, 2010, 2:36 pm
  Posted by Charlie on 2010-03-21 14:26:08

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