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 Extending tic-tac-toe (Posted on 2014-10-23)
In a standard 3x3 tic-ta-toe there are 8 distinct possibilities to create “three in a row”- 3 horizontal, 3 vertical and 2 diagonal.

How many ways are there in a three-dimensional 5x5x5 tic-tac-toe?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solutions | Comment 5 of 6 |
For different sizes n x n x n:

n ways
3 49
4 224
5 603
6 1264
7 2285
8 3744
9 5719

note the 3 x 3 x 3 case matches the formula from my first comment, where I thought the number in a row matched n.

from:

DefDbl A-Z
Dim crlf\$

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For n = 3 To 9
ct = 0
For layer = 1 To n
For x = 1 To n
For y = 1 To n
For vdiff = 0 To 2 Step 2
For xdiff = -2 To 2 Step 2
For ydiff = -2 To 2 Step 2
If vdiff <> 0 Or xdiff <> 0 Or ydiff <> 0 Then
If x + xdiff > 0 And x + xdiff <= n Then
If y + ydiff > 0 And y + ydiff <= n Then
If layer + vdiff > 0 And layer + vdiff <= n Then
good = 1 ' Now prevent double counting (two directions):
If vdiff = 0 And xdiff < 0 Then good = 0
If vdiff = 0 And xdiff = 0 And ydiff < 0 Then good = 0
If good Then
ct = ct + 1
End If
End If
End If
End If
End If
Next ydiff
Next xdiff
Next vdiff
Next y
Next x
Next layer
Text1.Text = Text1.Text & n & Str(ct) & crlf
Next n

Text1.Text = Text1.Text & crlf & "done"
End Sub

 Posted by Charlie on 2014-10-23 10:21:55

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