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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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Solution computer solution | Comment 1 of 7
    5   dim Used(9),Pv(6)
   10   for L=1 to 9
   15    Used(L)=1
   20    for S=1 to 9 step 2
   30     if Used(S)=0 then
   35      :Used(S)=1
   40      :for T=1 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=1 to 9 step 2
   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          :Prmcnt=0:for I=1 to 6:Pv(I)=0:next
   82          :if prmdiv(Least)=Least then Prmcnt=Prmcnt+1:Pv(1)=1:endif
   83          :if prmdiv(Slate)=Slate then Prmcnt=Prmcnt+1:Pv(2)=1:endif
   84          :if prmdiv(Stale)=Stale then Prmcnt=Prmcnt+1:Pv(3)=1:endif
   85          :if prmdiv(Steal)=Steal then Prmcnt=Prmcnt+1:Pv(4)=1:endif
   86          :if prmdiv(Taels)=Taels then Prmcnt=Prmcnt+1:Pv(5)=1:endif
   87          :if prmdiv(Tales)=Tales then Prmcnt=Prmcnt+1:Pv(6)=1:endif
   88          :if Prmcnt>4 then
   89            :print:print Least;Pv(1):print Slate;Pv(2):print Stale;Pv(3):pr
int Steal;Pv(4):print Taels;Pv(5):print Tales;Pv(6):print Prmcnt:Sct=Sct+1
   90          :endif
   91          :Used(E)=0
   92        :endif
   93      :next E
   94          :Used(A)=0
   95        :endif
   96      :next A
   97          :Used(T)=0
   98        :endif
   99      :next T
  100      :Used(S)=0
  110     :endif
  120    next S
  125    Used(L)=0
  130   next L
  150   print Sct
 
finds nine solutions:
 37612  0
 13627  1
 12637  1
 12763  1
 26731  1
 26371  1
 5
 41539  1
 34591  1
 39541  1
 39154  0
 95143  1
 95413  1
 5
 51439  1
 35491  1
 39451  1
 39145  0
 94153  1
 94513  1
 5
 53791  1
 95713  1
 91753  1
 91375  0
 17359  1
 17539  1
 5
 79813  1
 17839  1
 13879  1
 13987  0
 38971  1
 38791  1
 5
 73019  1
 17093  1
 19073  1
 19307  0
 90371  1
 90731  1
 5
 79031  1
 37019  1
 31079  1
 31907  1
 10973  1
 10793  0
 5
 87613  1
 18637  1
 13687  1
 13768  0
 36781  1
 36871  1
 5
 97213  1
 19237  1
 13297  1
 13729  1
 32791  0
 32971  1
 5
 9


 
The 1 or 0 next to each line indicates whether the number is or is not, respectively, a prime number.

So if there are nine solutions, what are the "three ways"?

 


  Posted by Charlie on 2010-03-20 13:59:49
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