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 Thrice three is nine (Posted on 2010-09-11)
Three 3-digit primes, all digits being distinct, sum up to a three digit number.
Can you find this number?

a. No zeroes allowed .
b. Zeroes, non-leading of course, can appear on both sides of the equation.

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 computer solution | Comment 1 of 5

10   A=99
20   repeat
30    A=nxtprm(A):Aa=cutspc(str(A))
40    Good=1
50    for I=1 to 2
60      if instr(mid(Aa,I+1,*),mid(Aa,I,1))>0 then Good=0
70    next I
80    if Good then
110      :B=A
120      :repeat
130      :B=nxtprm(B):Bb=cutspc(str(B))
140      :Good=1
145      :if instr(Aa,mid(Bb,3,1))>0 then Good=0:endif
150      :for I=1 to 2
160      :if instr(mid(Bb,I+1,*)+Aa,mid(Bb,I,1))>0 then Good=0:endif
170      :next I
180      :if Good then
210           :C=B
220           :repeat
230           :C=nxtprm(C):Cc=cutspc(str(C))
240           :Good=1
245           :if instr(Aa+Bb,mid(Cc,3,1))>0 then Good=0:endif
250           :for I=1 to 2
260           :if instr(mid(Cc,I+1,*)+Aa+Bb,mid(Cc,I,1))>0 then Good=0:endif
270           :next I
280           :if Good and A+B+C<1000 then print A;B;C,A+B+C:Ct=Ct+1:endif
310           :until C>999
320      :endif
330      :until B>999
340    :endif
350   until A>999
400   print Ct

produces

`    primes       sum 103  269  457   829 103  269  487   859 103  269  547   919 103  269  587   959 107  283  569   959 109  257  463   829 109  263  457   829 109  263  487   859 109  263  547   919 109  263  587   959 109  283  457   849 109  283  467   859 109  283  547   939 149  263  587   999 157  263  409   829 157  283  409   849 163  257  409   829 167  283  409   859 167  283  509   959 `

of which only  149 + 263 + 587 = 999 lacks a zero.

 Posted by Charlie on 2010-09-11 16:22:45

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