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|
REM Work out solutions to the "hex" problem. The idea here
REM is to find all the solutions to a magic square where the
REM numbers 1 to 19 have to be arranged in a hex pattern
REM so that all the straight lines add up to 38 thus:
REM
REM xx xx xx
REM xx xx xx xx
REM xx xx xx xx xx
REM xx xx xx xx
REM xx xx xx
:
threesize%=200
:
DIM jval%(threesize%), kval%(threesize%), nextpos%(threesize%)
DIM xlistpos%(19), used%(19), ring%(19), checks%(6,3), does%(6)
:
T=TIME
checks%(1,1)=8: checks%(1,2)=12: checks%(1,3)=18
checks%(2,1)=2: checks%(2,2)=10: checks%(2,3)=18
checks%(3,1)=4: checks%(3,2)=12: checks%(3,3)=13
checks%(4,1)=6: checks%(4,2)=10: checks%(4,3)=17
checks%(5,1)=2: checks%(5,2)=6: checks%(5,3)=14
checks%(6,1)=4: checks%(6,2)=8: checks%(6,3)=16
does%(1)=17
does%(2)=13
does%(3)=14
does%(4)=16
does%(5)=15
does%(6)=15
nosol%=0
num%=0
FOR I%=1 TO 19
used%(I%)=FALSE
xlistpos%(I%)=0
NEXT
:
FOR I%=3 TO 19
FOR J%=1 TO 19
IF I%<>J% THEN
FOR K%=3 TO 19
IF (K%<>J%) AND (K%<>I%) AND (I%+J%+K%=38) THEN
num%+=1
next%=num%
jval%(next%)=J%
kval%(next%)=K%
nextpos%(next%)=xlistpos%(I%)
xlistpos%(I%)=next%
ENDIF
NEXT
ENDIF
NEXT
NEXT
PRINT FNdec(num%,3);" number groups generated"
:
FOR I%=3 TO 19
P%=xlistpos%(I%)
used%(I%)=TRUE
WHILE P%<>0
J%=jval%(P%)
K%=kval%(P%)
used%(J%)=TRUE
used%(K%)=TRUE
ring%(1)=I%
ring%(2)=J%
curr%=2
PROCfillin(K%)
used%(J%)=FALSE
used%(K%)=FALSE
P%=nextpos%(P%)
ENDWHILE
used%(I%)=FALSE
NEXT
PRINT"There are";FNdec(nosol%,3);" solutions"
PRINT"Time taken: ";(TIME-T)/100;" seconds"
END
:
:
DEF FNdec(X%,W%)=RIGHT$(" "+STR$X%,W%)
:
:
DEF PROCblockin(target%)
LOCAL total%, poss%, I%
IF target%>5 THEN
IF (38-ring%(4)-ring%(8)-ring%(16))=ring%(15) THEN
poss%=1
WHILE used%(poss%)
poss%+=1
ENDWHILE
IF (38-ring%(11)-ring%(18)-ring%(15)-ring%(5))=poss% THEN
ring%(19)=poss%
nosol%+=1
PRINT"Solution no.";FNdec(nosol%,3)''
PRINT" ";FNdec(ring%(1),2);FNdec(ring%(2),4);FNdec(ring%(3),4)
PRINT" ";FNdec(ring%(12),2);FNdec(ring%(13),4);FNdec(ring%(14),4);FNdec(ring%(4),4)
PRINT" ";FNdec(ring%(11),2);FNdec(ring%(18),4);FNdec(ring%(19),4);FNdec(ring%(15),4);FNdec(ring%(5),4)
PRINT" ";FNdec(ring%(10),2);FNdec(ring%(17),4);FNdec(ring%(16),4);FNdec(ring%(6),4)
PRINT" ";FNdec(ring%(9),2);FNdec(ring%(8),4);FNdec(ring%(7),4)''
ENDIF
ENDIF
ELSE
total%=38
FOR I%=1 TO 3
total%=total%-ring%(checks%(target%,I%))
NEXT
IF (total%>0) AND (total%<20) THEN
IF NOT used%(total%) THEN
used%(total%)=TRUE
ring%(does%(target%))=total%
PROCblockin(target%+1)
used%(total%)=FALSE
ENDIF
ENDIF
ENDIF
ENDPROC
:
DEF PROCfillin(pi%)
LOCAL I%, pj%, pk%, pos1%, ptr%
ptr%=xlistpos%(pi%)
WHILE ptr%<>0
pj%=jval%(ptr%)
pk%=kval%(ptr%)
IF NOT used%(pj%) AND NOT used%(pk%) THEN
used%(pj%)=TRUE
used%(pk%)=TRUE
ring%(curr%+curr%-1)=pi%
ring%(curr%+curr%)=pj%
curr%+=1
IF curr%<7 THEN PROCfillin(pk%)
used%(pk%)=FALSE
used%(pj%)=FALSE
curr%-=1
ELSE
IF curr%=6 THEN
IF NOT used%(pj%) AND pk%=ring%(1) THEN
used%(pj%)=TRUE
ring%(11)=pi%
ring%(12)=pj%
FOR I%=1 TO 19
IF NOT used%(I%) THEN
ring%(18)=I%
used%(I%)=TRUE
PROCblockin(1)
used%(I%)=FALSE
ENDIF
NEXT
used%(pj%)=FALSE
ENDIF
ENDIF
ENDIF
ptr%=nextpos%(ptr%)
ENDWHILE
ENDPROC
|
