The first version of the below program was finding tens of thousands of solutions (minor variations, I guess you'd say) without evan exhausting those with 1 in the upper left corner (reserved for the lowest corner number in the grid, to avoid reflections and rotations). So the version below limits the number that are found with any given lowest corner. The highest of the lowest corners was found to be 15, though up to 17 was allowed for in the case of, say, corners being 17, 18, 19 and 20.
DefDbl A-Z
Dim crlf$, grid(6, 5), used(20), solct, innerct
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
Open "big difference.txt" For Output As #2
For upperleft = 1 To 17
innerct = 0
Text1.Text = Text1.Text & upperleft & crlf
grid(1, 1) = upperleft
used(upperleft) = 1
addOn 1, 2
used(upperleft) = 0
Next
Text1.Text = Text1.Text & crlf & solct & " done"
Close 2
End Sub
Sub addOn(row, col)
DoEvents
If innerct > 20 Then Exit Sub
For newnum = 1 To 20
If used(newnum) = 0 Then
good = 1
If row = 1 And col = 4 Or row = 5 And col = 4 Then If newnum < grid(1, 1) Then good = 0
If row = 5 And col = 1 Then If newnum < grid(1, 1) Or newnum < grid(1, 4) Then good = 0
If good Then
bad = 0
For dr = -1 To 1
For dc = -1 To 1
If dr <> 0 Or dc <> 0 Then
If grid(row + dr, col + dc) > 0 Then
If Abs(newnum - grid(row + dr, col + dc)) < 4 Then bad = 1: Exit For
End If
End If
Next
If bad Then Exit For
Next
If bad = 0 Then
grid(row, col) = newnum
used(newnum) = 1
If row = 5 And col = 4 Then
For r = 1 To 5
For c = 1 To 4
Print #2, mform(grid(r, c), "##0");
Next
Print #2,
Next
Print #2,
solct = solct + 1
innerct = innerct + 1
Else
r = row: c = col
c = c + 1: If c > 4 Then c = 1: r = r + 1
addOn r, c
End If
grid(row, col) = 0
used(newnum) = 0
End If
End If
End If
Next
End Sub
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
The sampling:
1 5 9 2
14 18 13 17
10 3 8 4
16 20 15 19
12 6 11 7
1 5 9 2
14 18 13 17
10 3 8 4
16 20 15 19
12 7 11 6
1 5 9 2
14 18 13 17
10 3 8 4
19 15 20 12
6 11 7 16
2 6 1 5
17 13 19 15
9 3 7 11
18 14 20 16
10 4 8 12
2 6 1 7
12 16 11 15
8 20 3 19
4 14 9 13
10 18 5 17
2 6 1 7
12 16 11 15
8 20 4 19
3 14 9 13
10 18 5 17
2 6 1 7
12 16 11 15
8 20 5 19
3 14 9 13
10 18 4 17
3 7 1 5
12 16 11 15
8 20 6 19
4 14 2 13
10 18 9 17
3 7 1 5
12 16 11 15
8 20 6 19
13 2 14 10
17 9 18 4
3 7 1 5
12 16 11 19
8 20 6 15
4 13 2 10
17 9 18 14
3 7 1 5
13 17 11 15
9 2 6 19
16 20 14 10
12 8 4 18
3 7 1 5
16 12 17 13
20 8 2 9
4 14 19 15
18 10 6 11
4 8 1 5
13 17 12 16
9 2 6 20
14 18 11 15
10 3 7 19
4 8 1 5
13 17 12 16
9 2 6 20
15 19 14 10
11 7 3 18
4 8 1 5
13 17 12 16
9 2 7 20
15 19 14 3
11 6 10 18
4 8 1 5
13 17 12 16
9 3 7 20
14 18 11 15
10 2 6 19
4 8 1 5
13 17 12 16
9 3 7 20
14 18 11 15
10 6 2 19
4 8 1 5
13 17 12 16
9 3 7 20
15 19 14 2
11 6 10 18
4 8 1 5
14 18 12 16
10 6 2 20
15 19 13 9
11 7 3 17
4 8 1 5
14 18 13 17
10 6 2 9
19 15 20 16
7 11 3 12
5 1 6 10
11 15 20 16
19 2 7 12
8 13 18 3
17 4 9 14
5 1 6 10
11 15 20 16
19 2 7 12
9 13 18 3
17 4 8 14
5 1 6 10
11 15 20 16
19 2 8 12
7 13 18 4
17 3 9 14
5 1 6 10
11 15 20 16
19 3 7 12
8 13 18 2
17 4 9 14
5 1 6 10
11 15 20 16
19 3 7 12
9 13 18 2
17 4 8 14
5 1 6 10
11 15 20 16
19 3 8 12
7 13 18 4
17 2 9 14
5 1 6 10
15 11 18 14
19 7 2 8
3 13 20 12
17 9 4 16
6 1 5 9
10 18 13 17
14 2 7 3
8 20 11 15
12 16 4 19
6 1 5 9
10 18 13 17
14 2 7 3
8 20 11 19
12 16 4 15
6 1 5 9
10 18 13 17
14 3 7 2
8 20 11 15
12 16 4 19
6 1 5 9
10 18 13 17
14 3 7 2
8 20 11 19
12 16 4 15
6 1 5 9
14 18 13 17
10 2 7 3
15 19 12 16
11 4 8 20
6 1 5 9
14 18 13 17
10 2 8 4
19 15 20 16
11 3 7 12
7 1 5 9
14 18 13 17
10 2 8 3
6 15 20 12
19 11 4 16
7 1 5 9
14 18 13 17
10 2 8 3
6 15 20 16
19 11 4 12
7 1 5 9
14 18 13 17
10 2 8 4
6 15 20 12
19 11 3 16
7 1 5 9
14 18 13 17
10 2 8 4
6 15 20 16
19 11 3 12
7 1 5 9
14 18 13 17
10 3 8 4
15 19 12 16
11 2 6 20
7 1 5 9
14 18 13 17
10 3 8 4
15 19 12 16
11 6 2 20
7 1 5 9
14 18 13 17
10 4 8 3
19 15 20 12
11 2 6 16
8 1 5 9
14 18 13 17
10 2 7 3
6 15 20 12
19 11 4 16
8 1 5 9
14 18 13 17
10 2 7 3
6 15 20 16
19 11 4 12
8 1 5 9
14 18 13 17
10 2 7 3
6 16 11 15
12 20 4 19
8 1 5 9
14 18 13 17
10 2 7 3
6 16 11 19
12 20 4 15
8 1 5 9
14 18 13 17
10 2 7 3
6 20 11 15
12 16 4 19
8 1 5 10
17 13 18 14
4 9 2 6
16 20 15 19
12 3 7 11
9 1 5 10
15 19 14 18
11 3 8 4
7 17 12 16
13 2 6 20
9 1 5 10
15 19 14 18
11 3 8 4
7 17 12 20
13 2 6 16
9 1 5 10
15 19 14 18
11 7 2 6
3 17 12 16
13 8 4 20
9 1 5 10
15 19 14 18
11 7 2 6
3 17 12 20
13 8 4 16
9 1 5 10
17 13 18 14
3 7 2 6
11 15 20 12
19 4 8 16
9 1 5 10
17 13 18 14
3 7 2 6
11 15 20 16
19 4 8 12
9 1 5 10
17 13 18 14
4 8 2 6
12 20 15 11
16 3 7 19
10 1 5 11
6 14 19 15
18 2 7 3
9 13 20 12
17 4 8 16
10 1 5 11
6 14 19 15
18 2 7 3
9 13 20 16
17 4 8 12
10 1 5 11
6 14 19 15
18 2 8 4
9 13 20 12
17 3 7 16
10 1 5 11
6 14 19 15
18 2 8 4
9 13 20 16
17 3 7 12
10 1 5 11
6 14 19 15
18 2 9 4
7 13 20 16
17 3 8 12
10 1 5 11
6 14 19 15
18 2 9 4
8 13 20 16
17 3 7 12
10 1 5 11
6 14 20 16
18 2 7 12
8 13 19 3
17 4 9 15
10 1 5 13
6 19 9 18
15 2 14 4
11 7 20 8
17 3 16 12
11 1 5 17
7 15 9 13
19 3 20 4
14 10 16 8
18 6 2 12
11 1 6 15
7 18 10 2
12 3 14 19
8 20 9 5
16 4 13 17
11 1 6 15
7 19 10 2
12 3 14 18
8 20 9 5
16 4 13 17
11 1 6 16
5 15 20 10
19 9 2 14
4 13 18 7
17 8 3 12
11 1 6 16
5 15 20 10
19 9 3 14
4 13 18 7
17 8 2 12
11 1 6 16
5 15 20 10
19 9 4 14
2 13 18 8
17 7 3 12
11 1 6 16
5 15 20 10
19 9 4 14
3 13 18 8
17 7 2 12
11 1 7 12
5 15 20 16
19 9 2 6
3 13 18 10
17 8 4 14
11 1 7 12
5 15 20 16
19 9 2 6
4 13 18 10
17 8 3 14
11 1 9 15
20 5 19 4
16 10 14 8
6 2 18 3
17 13 7 12
12 1 5 13
8 19 9 18
3 15 4 14
7 11 20 10
17 2 6 16
12 1 9 13
16 5 18 4
20 10 14 8
6 2 19 3
17 11 7 15
12 1 9 13
18 5 19 4
14 10 15 8
6 2 20 3
17 11 7 16
12 1 9 13
19 5 18 4
15 10 14 8
6 2 20 3
17 11 7 16
12 1 9 13
20 5 18 4
16 10 14 8
6 2 19 3
17 11 7 15
12 1 9 15
16 5 19 4
20 10 14 8
6 2 18 3
17 11 7 13
12 1 9 15
20 5 19 4
16 10 14 8
6 2 18 3
17 11 7 13
12 3 7 15
8 16 11 19
4 20 2 6
13 9 14 10
17 5 1 18
13 1 10 14
5 19 6 2
9 15 11 17
4 20 3 7
16 8 12 18
13 1 10 14
5 19 6 2
9 15 11 18
4 20 3 7
16 8 12 17
13 2 6 15
9 17 11 19
5 1 7 3
10 14 20 12
18 4 8 16
13 2 7 17
9 18 12 3
5 1 8 16
11 15 20 4
19 6 10 14
13 2 7 18
9 17 12 3
5 1 8 16
11 15 20 4
19 6 10 14
13 2 8 16
6 17 12 20
10 1 7 3
5 14 19 11
18 9 4 15
13 2 8 17
6 18 12 3
10 1 7 16
5 14 20 11
19 9 4 15
13 3 7 18
9 17 11 2
5 1 6 15
16 12 19 10
20 8 4 14
14 2 6 15
10 18 11 19
5 1 7 3
9 13 20 12
17 4 8 16
14 3 7 15
10 18 11 19
2 6 1 5
12 20 13 9
16 8 4 17
14 3 7 15
10 18 11 19
5 1 6 2
9 13 20 12
17 4 8 16
14 4 8 16
10 18 12 20
5 1 6 2
9 13 19 11
17 3 7 15
14 4 8 16
10 18 12 20
5 1 7 3
9 13 19 11
17 2 6 15
14 4 8 17
10 18 12 2
5 1 6 16
9 13 20 11
19 3 7 15
14 4 8 17
10 18 12 3
5 1 7 16
9 13 20 11
19 2 6 15
14 5 9 15
10 1 19 4
17 6 13 8
12 2 20 3
18 7 11 16
15 5 9 17
11 1 13 3
16 7 18 8
12 2 14 4
19 6 10 20
15 5 9 17
11 1 13 3
16 7 18 8
12 2 14 4
20 6 10 19
15 5 9 17
11 1 13 3
16 7 19 8
12 2 14 4
18 6 10 20
15 5 9 17
11 1 13 3
16 7 19 8
12 2 14 4
20 6 10 18
15 5 9 17
11 1 13 3
16 7 20 8
12 2 14 4
18 6 10 19
15 5 9 17
11 1 13 3
16 7 20 8
12 2 14 4
19 6 10 18
15 5 9 17
11 1 13 4
7 18 8 19
3 14 2 12
20 10 6 16
15 5 9 17
11 1 13 4
7 18 8 20
3 14 2 12
19 10 6 16
15 5 9 17
11 1 13 4
19 7 18 8
3 14 2 12
20 10 6 16
computer solutions
