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?

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 U
OK
run
 3  2  1  7  5
OK

So FOCUS is 32175.

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