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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

Comments: ( Back to comment list | You must be logged in to post comments.)
 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  1slate 17093  1stale 19073  1steal 19307  0taels 90371  1tales 90731  1leats 73091  1salet 10739  1setal 13907  1stela 19370  0teals 93071  0tesla 93170  0 8`
`least 73891  0slate 97813  1stale 91873  1steal 91387  1taels 18379  1tales 18739  0leats 73819  1salet 98731  1setal 93187  1stela 91378  0teals 13879  1tesla 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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