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 Primed Groups (Posted on 2010-09-19)

 No Solution Yet Submitted by brianjn No Rating

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 computer solution | Comment 1 of 3

DECLARE FUNCTION isPrime! (x!)
DATA      19,1,7,16,49
DATA      43,3,4,5,41
DATA      61,64,2,11,49
DATA      37,11,53,36,23
DATA      31,25,29,59,9

FOR r = 1 TO 5
FOR c = 1 TO 5
NEXT
NEXT

CLS

DIM SHARED prime(50)

DATA    2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59
DATA    61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131
DATA    137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197
DATA    199 , 211 , 223 , 227 , 229

FOR i = 1 TO 50: READ prime(i): NEXT

FOR r = 1 TO 5
FOR c = 1 TO 5
gr2(r, c) = gr1(r - 1, c) + gr1(r + 1, c) + gr1(r, c - 1) + gr1(r, c + 1)
LOCATE r + 3, c * 8
IF isPrime(gr2(r, c)) THEN PRINT gr2(r, c); :  ELSE PRINT "  .  ";
NEXT
NEXT

FUNCTION isPrime (x)
good = 0
FOR i = 1 TO 50
IF x = prime(i) THEN good = 1: EXIT FOR
NEXT
isPrime = good
END FUNCTION

shows

` .      29       .      61       .83       .      17       .      103 .       .       .       .       .103     179      .       .       . .      71      137      .       .`

where only the prime totals are shown for the resulting matrix. There are nine of them.

Then:

`   10   dim Grnum(10),H(10),Used(10)   20   data 17,29,61,71,83,103,103,137,179   30   for I=1 to 9:read Grnum(I):Ovrtot=Ovrtot+Grnum(I):next   50   H(1)=1:gosub *Addon2(2)  999   end 2000   *Addon2(Ptr) 2010   local I,J,Strt 2015   if Ptr @ 3=1 then Strt=H(Ptr-3)+1:else Strt=H(Ptr-1)+1 2020   for I=Strt to 9 2021    if Used(I)>0 then goto *NotThis 2025    if Ptr @ 3=0 and prmdiv(Grnum(H(Ptr-2))+Grnum(H(Ptr-1))+Grnum(I))<Grnum(H(Ptr-2))+Grnum(H(Ptr-1))+Grnum(I) then goto *NotThis 2030    H(Ptr)=I:Used(I)=1 2040    if Ptr=9 then 2090             :for J=1 to 9:print Grnum(H(J));:next:print 2091    :for J1=0 to 6 step 3:Tt=0:for J2=1 to 3:Tt=Tt+Grnum(H(J1+J2)):next:print Tt;:next:print:print 2100     :else 2110        :gosub *Addon2(Ptr+1) 2120     Used(I)=0 2125   *NotThis 2130   next 2190   return  prints   17  29  61  71  83  103  103  137  179  107  257  419   17  29  61  71  83  103  103  137  179  107  257  419   17  29  103  61  83  137  71  103  179  149  281  353   17  29  103  61  83  137  71  103  179  149  281  353   17  61  179  29  103  137  71  83  103  257  269  257   17  61  179  29  103  137  71  83  103  257  269  257   17  71  103  29  61  83  103  137  179  191  173  419   17  71  103  29  103  179  61  83  137  191  311  281   17  71  103  29  61  83  103  137  179  191  173  419   17  71  103  29  103  179  61  83  137  191  311  281   17  103  137  29  61  83  71  103  179  257  173  353   17  103  137  29  61  179  71  83  103  257  269  257   17  103  137  29  61  83  71  103  179  257  173  353   17  103  137  29  61  179  71  83  103  257  269  257  `

In each solution, the first three are the first group; the middle three are the second group; and the last three are the third group.

Each solution is listed twice, as the two 103's are considered distinct by the program. So there are actually 7 solutions, not 14.

The grouping totals are shown in the line below the groupings.

 Posted by Charlie on 2010-09-20 14:21:32

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