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 Focusing Upon Couscous (Posted on 2008-11-10)
In the following statements, each of the capital letters in bold represent a different decimal digit from 1 to 9.

COUSCOUS is an 8-digit positive integer none of whose digits is composite and it is divisible without remainder by each of the primes CU, S, F, CFU and UF but not by the prime number CC.

What is the number represented by FOCUS?

 See The Solution Submitted by K Sengupta No Rating

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 computer solution | Comment 1 of 3
`list   10     dim Taken(9)   20     C=1:Taken(1)=1   30     for U=3 to 7 step 4   40       Taken(U)=1   50     for S=2 to 7   60     if Taken(S)=0 and prmdiv(S)=S then   70     :Taken(S)=1   80     :for F=2 to 7   90       :if Taken(F)=0 and prmdiv(F)=F then  100         :Taken(F)=1  110         :Cfu=C*100+F*10+U  120         :Uf=U*10+F  130         :Cu=C*10+U  140         :if prmdiv(Cfu)=Cfu and prmdiv(Uf)=Uf and prmdiv(Cu)=Cu then  141   :for O=2 to 7  142    :if Taken(O)=0 and prmdiv(O)=O then  143       :Couscous=10001000+1000100*O+100010*U+10001*S  144       :if Couscous@Cu=0 and Couscous@S=0 and Couscous@F=0 then  145         :if Couscous@Cfu=0 and Couscous@Uf=0 and Couscous@11>0 then  150           :print F;O;C;U;S  156         :endif  157       :endif  158    :endif  159   :next O  160         :endif  170         :Taken(F)=0  180       :endif  190     :next F  200     :Taken(S)=0  210     :endif  220     next S  230     Taken(U)=0  240     next UOKrun 3  2  1  7  5OK`

So FOCUS is 32175.

 Posted by Charlie on 2008-11-10 17:53:18

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