In the following grid:
(1) The numbers in each column form an increasing arithmetic sequence
(2) The numbers in each row form an increasing arithmetic sequence
(3) The X's in each spot indicate how many digits are in the number
(4) A is at least 1200
(5) B is at least 2900
+---+---+----+----+----+----+----+----+
| 0| XX| XX| XX| XX| XX| XX| XXX|
+---+---+----+----+----+----+----+----+
| XX|XXX| XXX| XXX| XXX| XXX| XXX| XXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX| XXX| XXX| XXX| XXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX| XXX| XXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX| XXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| XXX|XXXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX|XXXX|XXXX|XXXX|XXXX|XXXX|XXXX|
+---+---+----+----+----+----+----+----+
|XXX|XXX| A|XXXX|XXXX|XXXX|XXXX| B|
+---+---+----+----+----+----+----+----+
Reconstruct the grid.
An analytic solution is preferred.
DefDbl A-Z
Dim crlf$, grid(8, 8)
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
grid(1, 1) = 0
For b = 2900 To 20000
grid(8, 8) = b
For a = 1200 To 1897
grid(8, 3) = a
row8incr = (b - a) / 5
If row8incr = Int(row8incr) Then
If a - row8incr < 1000 And a - 2 * row8incr > 99 And a + row8incr > 999 And b - row8incr < 10000 Then
For i = 1 To 7
grid(8, i) = a + row8incr * (i - 3)
Next
For ur = 100 To 999
row1incr = ur / 7
col8incr = (b - ur) / 7
If row1incr = Int(row1incr) And col8incr = Int(col8incr) Then
If ur + 2 * col8incr < 1000 And ur + 3 * col8incr > 999 And ur - row1incr < 100 Then
For i = 1 To 7
grid(i, 8) = ur + (i - 1) * col8incr
Next
If grid(8, 1) Mod 7 = 0 Then
col1incr = grid(8, 1) / 7
If col1incr > 10 And col1incr < 100 Then
If 2 * col1incr > 99 Then
For i = 2 To 7
grid(i, 1) = (i - 1) * col1incr
Next
good = 1
For row = 2 To 7
Select Case row
Case 2, 3
last3 = 8
Case 4
last3 = 6
Case 5
last3 = 4
Case 6
last3 = 3
Case 7
last3 = 2
End Select
rowincr = (grid(row, 8) - grid(row, 1)) / 7
If rowincr <> Int(rowincr) Then
good = 0: Exit For
End If
If grid(row, 1) + rowincr < 100 Or grid(row, 1) + (last3 - 1) * rowincr > 999 Then
good = 0: Exit For
End If
If row > 3 Then
If grid(row, 1) + rowincr * last3 < 1000 Then
good = 0: Exit For
End If
End If
For cl = 2 To 7
grid(row, cl) = grid(row, 1) + (cl - 1) * rowincr
Next
Next row
If good Then
For cl = 2 To 7
grid(1, cl) = (cl - 1) * row1incr
Next
GoSub showit
End If
End If
End If
End If
End If
End If
Next ur
End If
End If
Next a
Next b
Text1.Text = Text1.Text & "done"
Exit Sub
showit:
Text1.Text = Text1.Text & mform(a, "#####0") & mform(b, "#####0") & crlf
For rw = 1 To 8
For cl = 1 To 8
Text1.Text = Text1.Text & mform(grid(rw, cl), "####0")
Next: Text1.Text = Text1.Text & crlf
Next: Text1.Text = Text1.Text & crlf
DoEvents
sctr = sctr + 1: If sctr > 10 Then Exit Sub
Return
End Sub
finds
1220 2905
0 15 30 45 60 75 90 105
78 139 200 261 322 383 444 505
156 263 370 477 584 691 798 905
234 387 540 693 846 999 1152 1305
312 511 710 909 1108 1307 1506 1705
390 635 880 1125 1370 1615 1860 2105
468 759 1050 1341 1632 1923 2214 2505
546 883 1220 1557 1894 2231 2568 2905
the first line showing A and B. After that is the whole grid.
The program did not have to check the vertical columns (other that the first and last) for being in arithmetic progression; that came about automatically from the horizontal considerations together with the beginning and end column.
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Posted by Charlie
on 2014-06-12 23:44:27 |
The program method
