Given set of
fifteen integers
(1 to 15)
.
Erase 3 numbers so that remaining integers can be arranged as a
3 by 4 array in which
the sum of the numbers in each row is a certain Sr and in each of the
columns a certain Sc.
Present the triplet you have chosen and one of the possible arrangements.
D4. Bonus question:
How many distinct solutions are there?
DefDbl A-Z
Dim crlf$, used(15), grid(3, 4), row1tot, col1tot, solct
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
Open "c:VB5 projects loobleone triplet out.txt" For Output As #2
addOn 1, 1
Close
Text1.Text = Text1.Text & solct & crlf & " done"
End Sub
Sub addOn(row, col)
DoEvents
For newnum = 1 To 15
If used(newnum) = 0 Then
If row = 1 And col = 4 Then
Text2.Text = grid(1, 1) & Str(grid(1, 2)) & Str(grid(1, 3)) & Str(newnum)
End If
good = 1
If col = 4 Then
tot = grid(row, 1) + grid(row, 2) + grid(row, 3) + newnum
If row > 1 Then If tot <> row1tot Then good = 0
If row = 1 Then row1tot = tot
End If
If row = 3 Then
tot = grid(1, col) + grid(2, col) + newnum
If col > 1 Then If tot <> col1tot Then good = 0
If col = 1 Then col1tot = tot
End If
If row = 1 And col > 1 And newnum < grid(row, col - 1) Then good = 0
If col = 1 And row > 1 And newnum < grid(row - 1, col) Then good = 0
If good Then
grid(row, col) = newnum
used(newnum) = 1
If row = 3 And col = 4 Then
For r = 1 To 3
For c = 1 To 4
Print #2, Mid("123456789ABCDEF", grid(r, c), 1);
Next
Print #2, " "; row1tot; col1tot
Next
Print #2,
solct = solct + 1
Else
c = col + 1
If c > 4 Then c = 1: r = row + 1 Else r = row
addOn r, c
End If
used(newnum) = 0
End If
End If
Next
End Sub
finds there are 108 distinct solutions in which the columns are in order of ascending top numbers and the rows are in ascending order of leftmost number. The rows can be arranged in 3! = 6 ways, and the columns in 4! = 24 ways, so the total distinct solutions is 108 * 6 * 24 = 15,552. So you can see why it saves computation time to find only the 108.
While the arrays are given in hex below, for conciseness, the totals are of course in decimal:
12EF 32 24
B975 32 24
CD34 32 24
-----------------
12EF 32 24
BD35 32 24
C974 32 24
-----------------
13DF 32 24
9A67 32 24
EB52 32 24
-----------------
13DF 32 24
9B57 32 24
EA62 32 24
-----------------
13DF 32 24
B795 32 24
CE24 32 24
-----------------
13DF 32 24
BE25 32 24
C794 32 24
-----------------
14AD 28 21
8695 28 21
CB23 28 21
-----------------
14AD 28 21
9586 28 21
BC32 28 21
-----------------
14CF 32 24
97A6 32 24
ED23 32 24
-----------------
14CF 32 24
A697 32 24
DE32 32 24
-----------------
14CF 32 24
A976 32 24
DB53 32 24
-----------------
14CF 32 24
AB56 32 24
D973 32 24
-----------------
14DE 32 24
8B67 32 24
F953 32 24
-----------------
14DE 32 24
B597 32 24
CF23 32 24
-----------------
158E 28 21
76B4 28 21
DA23 28 21
-----------------
15BF 32 24
96A7 32 24
ED32 32 24
-----------------
15BF 32 24
9D37 32 24
E6A2 32 24
-----------------
15BF 32 24
A796 32 24
DC43 32 24
-----------------
15BF 32 24
AC46 32 24
D793 32 24
-----------------
16AF 32 24
95B7 32 24
ED32 32 24
-----------------
16AF 32 24
97C4 32 24
EB25 32 24
-----------------
16AF 32 24
9D37 32 24
E5B2 32 24
-----------------
16AF 32 24
BE52 32 24
C497 32 24
-----------------
16BE 32 24
8D47 32 24
F593 32 24
-----------------
179F 32 24
A5B6 32 24
DC43 32 24
-----------------
179F 32 24
A6C4 32 24
DB35 32 24
-----------------
179F 32 24
AC46 32 24
D5B3 32 24
-----------------
179F 32 24
B3D5 32 24
CE24 32 24
-----------------
179F 32 24
BD53 32 24
C4A6 32 24
-----------------
179F 32 24
BE25 32 24
C3D4 32 24
-----------------
17AE 32 24
B498 32 24
CD52 32 24
-----------------
17BD 32 24
85A9 32 24
FC32 32 24
-----------------
17BD 32 24
8C39 32 24
F5A2 32 24
-----------------
17BD 32 24
8CA2 32 24
F539 32 24
-----------------
17BD 32 24
8E46 32 24
F395 32 24
-----------------
17BD 32 24
9F35 32 24
E2A6 32 24
-----------------
23AD 28 21
8E51 28 21
B467 28 21
-----------------
23BC 28 21
6895 28 21
DA14 28 21
-----------------
23BC 28 21
9568 28 21
AD41 28 21
-----------------
23CF 32 24
97B5 32 24
DE14 32 24
-----------------
23CF 32 24
9A58 32 24
DB71 32 24
-----------------
23DE 32 24
79A6 32 24
FC14 32 24
-----------------
23DE 32 24
7A69 32 24
FB51 32 24
-----------------
23DE 32 24
7B59 32 24
FA61 32 24
-----------------
23DE 32 24
A679 32 24
CF41 32 24
-----------------
24CE 32 24
95B7 32 24
DF13 32 24
-----------------
24CE 32 24
9F17 32 24
D5B3 32 24
-----------------
25AF 32 24
9C38 32 24
D7B1 32 24
-----------------
25BE 32 24
76A9 32 24
FD31 32 24
-----------------
25BE 32 24
79C4 32 24
FA16 32 24
-----------------
25BE 32 24
7D39 32 24
F6A1 32 24
-----------------
25BE 32 24
94C7 32 24
DF13 32 24
-----------------
25BE 32 24
97A6 32 24
DC34 32 24
-----------------
25BE 32 24
9F17 32 24
D4C3 32 24
-----------------
25BE 32 24
A697 32 24
CD43 32 24
-----------------
25BE 32 24
AF61 32 24
C479 32 24
-----------------
25CD 32 24
89B4 32 24
EA17 32 24
-----------------
269F 32 24
87C5 32 24
EB34 32 24
-----------------
26AE 32 24
75B9 32 24
FD31 32 24
-----------------
26AE 32 24
7D39 32 24
F5B1 32 24
-----------------
26AE 32 24
7DB1 32 24
F539 32 24
-----------------
28AC 32 24
9F35 32 24
D1B7 32 24
-----------------
28BF 36 27
C5A9 36 27
DE63 36 27
-----------------
34BE 32 24
9F62 32 24
C578 32 24
-----------------
34CD 32 24
697A 32 24
FB51 32 24
-----------------
34CD 32 24
6B5A 32 24
F971 32 24
-----------------
34CD 32 24
75B9 32 24
EF12 32 24
-----------------
34CD 32 24
79A6 32 24
EB25 32 24
-----------------
34CD 32 24
7F19 32 24
E5B2 32 24
-----------------
34CD 32 24
A679 32 24
BE52 32 24
-----------------
359F 32 24
76B8 32 24
ED41 32 24
-----------------
359F 32 24
7D48 32 24
E6B1 32 24
-----------------
359F 32 24
7DB1 32 24
E648 32 24
-----------------
359F 32 24
A6E2 32 24
BD17 32 24
-----------------
359F 32 24
AC28 32 24
B7D1 32 24
-----------------
35BD 32 24
679A 32 24
FC41 32 24
-----------------
35BD 32 24
6AC4 32 24
F917 32 24
-----------------
35BD 32 24
6C4A 32 24
F791 32 24
-----------------
35BD 32 24
74C9 32 24
EF12 32 24
-----------------
35BD 32 24
7F19 32 24
E4C2 32 24
-----------------
35BD 32 24
9F71 32 24
C46A 32 24
-----------------
36CF 36 27
A8B7 36 27
ED45 36 27
-----------------
36CF 36 27
B7A8 36 27
DE54 36 27
-----------------
36DE 36 27
9AC5 36 27
FB28 36 27
-----------------
379D 32 24
65BA 32 24
FC41 32 24
-----------------
379D 32 24
6C4A 32 24
F5B1 32 24
-----------------
379D 32 24
A2E6 32 24
BF15 32 24
-----------------
379D 32 24
AF16 32 24
B2E5 32 24
-----------------
389C 32 24
AF25 32 24
B1D7 32 24
-----------------
45DE 36 27
8AB7 36 27
FC36 36 27
-----------------
45DE 36 27
B78A 36 27
CF63 36 27
-----------------
468E 32 24
95F3 32 24
BD17 32 24
-----------------
46AC 32 24
5BD3 32 24
F719 32 24
-----------------
46AC 32 24
7F91 32 24
D35B 32 24
-----------------
46AC 32 24
93D7 32 24
BF15 32 24
-----------------
46AC 32 24
9F17 32 24
B3D5 32 24
-----------------
478D 32 24
93F5 32 24
BE16 32 24
-----------------
479C 32 24
53DB 32 24
FE21 32 24
-----------------
479C 32 24
5BE2 32 24
F61A 32 24
-----------------
479C 32 24
5E2B 32 24
F3D1 32 24
-----------------
479C 32 24
6FA1 32 24
E25B 32 24
-----------------
489B 32 24
7EA1 32 24
D25C 32 24
-----------------
56AB 32 24
73D9 32 24
CF14 32 24
-----------------
56AB 32 24
7F19 32 24
C3D4 32 24
-----------------
579B 32 24
62EA 32 24
DF13 32 24
-----------------
579B 32 24
6F1A 32 24
D2E3 32 24
-----------------
589A 32 24
71DB 32 24
CF23 32 24
-----------------
59AC 36 27
8FB2 36 27
E36D 36 27
-----------------
Jer's solution arranged above is the:
158E 28 21
76B4 28 21
DA23 28 21
with the columns rearranged and the bottom two rows reversed.
Edited on June 16, 2015, 3:08 pm
|
|
Posted by Charlie
on 2015-06-16 15:05:58 |
computer solution
