An unlucky gardener planted a 10x10 square array of 100 old seeds out in the garden. Only 5 of these seeds have germinated including one at the southwest corner (0,0) where a slug is currently reducing it to ground level.
When it finishes it will head directly to the next closest doomed plant. After it eats that one it will again leave a slime trail to the closest remaining plant and so on until the garden is no more.
Where are the 4 remaining seedlings if the path crawled by the slug is the longest possible and it never has to choose between two equidistant snacks?
Note: Although the slug will never have to choose between two equidistant seedlings, this doesn't imply that no two are equidistant.
Next find the locations if 6 seedlings had germinated instead of 5.
(In reply to
re: Nicely done -- 2 thru 6 seedlings by Charlie)
Even a conversion to VB from QB didn't help that much. It took a couple of hours to find the solution for 7 seedlings, which I've added to the list below:
0 0 9 9 12.72792206135786
0 0 9 0 1 9 21.0415945787923
0 0 7 5 9 0 0 9 26.71541213553499
0 0 6 5 9 9 9 0 0 8 33.85184425469895
0 0 6 5 5 9 9 9 9 0 0 8 36.97494988031661
0 0 7 3 8 6 5 6 9 9 9 0 0 8 39.8196453448246
VERSION 5.00
Begin VB.Form Form1
AutoRedraw = -1 'True
Caption = "Form1"
ClientHeight = 6255
ClientLeft = 60
ClientTop = 450
ClientWidth = 9405
LinkTopic = "Form1"
ScaleHeight = 6255
ScaleWidth = 9405
StartUpPosition = 3 'Windows Default
Begin VB.CommandButton Command1
Caption = "Command1"
Height = 855
Left = 7080
TabIndex = 0
Top = 240
Width = 1935
End
End
Attribute VB_Name = "Form1"
Attribute VB_GlobalNameSpace = False
Attribute VB_Creatable = False
Attribute VB_PredeclaredId = True
Attribute VB_Exposed = False
Dim n
Dim curX(12), curY(12), curDist(12), curTot(12)
Dim hldX(12), hldY(12), hldDist(12), hldTot
Sub place(lvl)
DoEvents
For r = 0 To 9
stC = 0: If lvl = 2 Then stC = r
For c = stC To 9
For pLvl = 1 To lvl - 2
dist = Sqr((r - curY(pLvl)) * (r - curY(pLvl)) + (c - curX(pLvl)) * (c - curX(pLvl)))
If dist <= curDist(pLvl + 1) Then GoTo notThis
Next pLvl
dist = Sqr((r - curY(lvl - 1)) * (r - curY(lvl - 1)) + (c - curX(lvl - 1)) * (c - curX(lvl - 1)))
If dist = 0 Then GoTo notThis
curX(lvl) = c
curY(lvl) = r
curDist(lvl) = dist
curTot(lvl) = curTot(lvl - 1) + dist
If lvl = n Then
If curTot(lvl) > hldTot Then
Cls
For i = 1 To n
hldX(i) = curX(i): Print hldX(i);
hldY(i) = curY(i): Print hldY(i); " ";
hldDist(i) = curDist(i)
Next
hldTot = curTot(lvl)
Print hldTot
End If
Else
place lvl + 1
End If
notThis:
Next c
Next r
End Sub
Private Sub Command1_Click()
Form1.MousePointer = vbHourglass
curX(1) = 0
curY(1) = 0
curDist(1) = 0
curTot(1) = 0
n = 7
place 2
Print: Print "done"
Form1.MousePointer = vbDefault
End Sub
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Posted by Charlie
on 2006-06-26 13:47:48 |
re(2): Nicely done -- now through 7 seedlings
