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 Twisted TALES (Posted on 2010-03-20)
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 No Rating

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 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):print 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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