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.

(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