Problem :
Find the largest
( see topographical model section 1 )
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Section Below … Code for F1
Compiler …
Order
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///////////////////////////////////////////////////////////////////////////////
// Looking for Largest
//
// 8 - 3 - 2008
pred Magic5Assoc(filter:<I) iff
ms::[0..48]->>L[1..49] &
ms = [ a1, a2, a3, a4, a5, a6, a7,
b1, b2, b3, b4, b5, b6, b7,
c1, c2, c3, c4, c5, c6, c7,
d1, d2, d3, d4, d5, d6, d7,
e1, e2, e3, e4, e5, e6, e7,
f1, f2, f3, f4, f5, f6, f7,
g1, g2, g3, g4, g5, g6, g7
] &
a1 + a2 + a3 + a4 + a5 + a6 + a7 = 175 &
b1 + b2 + b3 + b4 + b5 + b6 + b7 = 175 &
c1 + c2 + c3 + c4 + c5 + c6 + c7 = 175 &
d1 + d2 + d3 + d4 + d5 + d6 + d7 = 175 &
e1 + e2 + e3 + e4 + e5 + e6 + e7 = 175 &
f1 + f2 + f3 + f4 + f5 + f6 + f7 = 175 &
g1 + g2 + g3 + g4 + g5 + g6 + g7 = 175 &
a1 + b1 + c1 + d1 + e1 + f1 + g1 = 175 &
a2 + b2 + c2 + d2 + e2 + f2 + g2 = 175 &
a3 + b3 + c3 + d3 + e3 + f3 + g3 = 175 &
a4 + b4 + c4 + d4 + e4 + f4 + g4 = 175 &
a5 + b5 + c5 + d5 + e5 + f5 + g5 = 175 &
a6 + b6 + c6 + d6 + e6 + f6 + g6 = 175 &
a7 + b7 + c7 + d7 + e7 + f7 + g7 = 175 &
a1 + b2 + c3 + d4 + e5 + f6 + g7 = 175 &
a7 + b6 + c5 + d4 + e3 + f2 + g1 = 175 &
////////////////////////////////////// external values
a1 = 2 &
a7 = 7 &
g1 = 6 &
g7 = 5 &
////////////////////////////////////// barrier values
a2 > 25 &
a3 = 36 &
a4 = 35 &
a5 = 34 &
b1 = 33 &
b6 > 26 &
c1 = 39 &
c7 = 29 &
d1 = 38 &
d7 = 27 &
f2 > 26 &
f6 > 26 &
g3 = 40 &
g4 = 25 &
g6 = 44 &
///////////////////////////////////////// island values
c3 > 26 &
c4 = 26 &
d3 > 25 &
d4 = 47 &
d5 = 31 &
e4 = 30 &
/////////////////////////////////// Moat values
b2 < 26 &
b3 < 26 &
b4 < 26 &
b5 < 26 &
c2 < 26 &
c5 < 26 &
c6 < 26 &
d2 < 26 &
d6 < 26 &
e2 < 26 &
e3 < 26 &
e5 = 49 &
e6 < 26 &
f3 < 26 &
f4 < 26 &
f5 < 26 &
////////////////////////////////// looking for 6th interior "island" cell
// d3 = 26 &
if filter <> 0 then
Filter(ms)
else
PrettyPrintA(ms,0)
end
///////////////////////////////////////////////////////////////////////////////
local proc Filter(ms:<[0..48]->>L[1..49]) iff
ms = [ a1, a2, a3, a4, a5, a6, a7,
b1, b2, b3, b4, b5, b6, b7,
c1, c2, c3, c4, c5, c6, c7,
d1, d2, d3, d4, d5, d6, d7,
e1, e2, e3, e4, e5, e6, e7,
f1, f2, f3, f4, f5, f6, f7,
g1, g2, g3, g4, g5, g6, g7
] &
if b2 = b2
then
PrettyPrintA(ms,0)
else
false // you may want to change this to "true" (or comment out)
end
///////////////////////////////////////////////////////////////////////////////
pred Magic5AssocPan() iff
ms::[0..48]->>L[1..49] &
ms = [ a1, a2, a3, a4, a5, a6, a7,
b1, b2, b3, b4, b5, b6, b7,
c1, c2, c3, c4, c5, c6, c7,
d1, d2, d3, d4, d5, d6, d7,
e1, e2, e3, e4, e5, e6, e7,
f1, f2, f3, f4, f5, f6, f7,
g1, g2, g3, g4, g5, g6, g7
] &
b2 = b2 &
PrettyPrintA(ms,0)
///////////////////////////////////////////////////////////////////////////////
local proc PrettyPrintA(ms:<[0..48]->>L[1..49], i:<I) iff
if i < 7 then
j = i * 7 &
Print('\n') &
PrintDigit(ms(j)) &
PrintDigit(ms(j+1)) &
PrintDigit(ms(j+2)) &
PrintDigit(ms(j+3)) &
PrintDigit(ms(j+4)) &
PrintDigit(ms(j+5)) &
PrintDigit(ms(j+6)) &
PrettyPrintA(ms,i+1)
else
Print('\n')
end
local proc PrintDigit(d:<L) iff
if d < 10 then
Print(' ',d,' ')
else
Print(d,' ')
End
In the above section … you
do not have to KNOW ANY PROGRAMING
all you have to do
Is put a educated guess as
to the values for about half the cells … and the program .. will
Generate solutions in a
reasonable amount of time for rest of the square ..
Perhaps it is like finding
the square root with a calculator … just push the buttons and let the
Calculator do its work ….
Add additional constraints ( initial
guess)
Looking at this example I fooled around with the parameters and was able to produce a example with 5 cells in the interior being island cells
What usually happens next .. is I will get excited about my work and email it to Francis Gaspalou . He will take pity on my floundering around and usually send me the general solution with the maximum number of cells possible … (see maximum water retention for order 5 magic square)
Adjusting the parameters and looking for solutions ….
1 46 36 35 34 14 9
48 24 17 6 11 47 22
39 20 32 26 16 13 29
38 2 28 45 31 4 27
37 19 10 30 21 15 43
5 41 12 8 18 49 42
7 23 40 25 44 33 3
___ Solution: 1 __________________________________
1 46 36 35 34 17 6
48 20 18 15 11 47 16
39 12 32 26 23 14 29
38 4 28 42 31 5 27
37 7 13 30 21 24 43
9 41 8 2 22 49 44
3 45 40 25 33 19 10
___ Solution: 2 __________________________________
1 46 36 35 34 13 10
49 24 20 9 11 47 15
39 16 33 26 18 14 29
38 4 28 45 31 2 27
37 23 6 30 17 19 43
3 41 12 5 22 48 44
8 21 40 25 42 32 7
___ Solution: 3 __________________________________
1 46 36 35 34 15 8
48 20 18 13 12 47 17
39 9 32 26 19 21 29
38 3 28 42 31 6 27
37 11 16 30 24 14 43
10 41 5 4 22 49 44
2 45 40 25 33 23 7
___ Solution: 4 __________________________________
1 46 36 35 34 18 5
44 24 21 11 12 47 16
39 14 32 26 20 15 29
38 4 28 45 31 2 27
37 13 10 30 19 23 43
9 41 8 3 17 48 49
7 33 40 25 42 22 6
___ Solution: 5 __________________________________
1 46 36 35 34 18 5
44 24 21 11 12 47 16
39 15 32 26 20 14 29
38 4 28 45 31 2 27
37 23 10 30 19 13 43
9 41 8 3 17 48 49
7 22 40 25 42 33 6
___ Solution: 6 __________________________________
1 46 36 35 34 16 7
48 24 14 8 12 47 22
39 23 33 26 15 10 29
38 2 28 45 31 4 27
37 19 11 30 18 17 43
3 41 13 6 21 49 42
9 20 40 25 44 32 5
___ Solution: 7 __________________________________
1 46 36 35 34 16 7
48 24 14 8 12 47 22
39 23 33 26 15 10 29
38 4 28 45 31 2 27
37 17 11 30 18 19 43
3 41 13 6 21 49 42
9 20 40 25 44 32 5
___ Solution: 8 __________________________________
1 46 36 35 34 13 10
48 23 20 8 12 47 17
39 14 33 26 16 18 29
38 4 28 45 31 2 27
37 15 7 30 19 24 43
3 41 11 6 21 49 44
9 32 40 25 42 22 5
___ Solution: 9 __________________________________
1 46 36 35 34 8 15
48 24 16 17 12 47 11
39 13 42 26 23 3 29
38 14 28 33 31 4 27
37 18 6 30 21 20 43
2 41 7 9 22 49 45
10 19 40 25 32 44 5
___ Solution: 10 __________________________________
1 46 36 35 34 12 11
49 24 18 9 13 47 15
39 10 32 26 16 23 29
38 4 28 45 31 2 27
37 17 7 30 19 22 43
3 41 14 5 20 48 44
8 33 40 25 42 21 6