perplexus.info :: General : Counting Ten Segment Paths

Counting Ten Segment Paths (Posted on 2016-02-19)

Multiple paths can be drawn on the grid below following along ten of the twelve segments but never using any segment twice.

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How many such paths are there?

No Solution Yet Submitted by Brian Smith

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re: As many as I found

| Comment 3 of 6 |

(In reply to As many as I found by Jer)

Using only what on Jer's diagram (assuming the first f should be e) would start hk, I get the following paths,

hkifcadgjl  be
hkifcadgeb  jl
hkifcabegd  jl
hkifcabejl  dg
hkidacfgjl  be
hkidacfgeb  jl
hkidbegfca  jl
hkigebacfd  jl
hkigebdfca  jl
hkljgfcadi  be
hkljgfcabe  di
hkljgdacfi  be
hkljebacfi  dg
hkljebacfd  gi
hkljebacfg  di
hkljebdfca  gi

showing the missing segments after the path,

from the following segment of my computer results:

01,00,10,11,01,02,12,11,21,20,10,

01,00,10,11,01,02,12,11,21,22,12,

01,00,10,11,01,02,12,22,21,11,12,

01,00,10,11,01,02,12,22,21,20,10,

01,00,10,11,12,02,01,11,21,20,10,

01,00,10,11,12,02,01,11,21,22,12,

01,00,10,11,12,22,21,11,01,02,12,

01,00,10,11,21,22,12,02,01,11,12,

01,00,10,11,21,22,12,11,01,02,12,

01,00,10,20,21,11,01,02,12,11,10,

01,00,10,20,21,11,01,02,12,22,21,

01,00,10,20,21,11,12,02,01,11,10,

01,00,10,20,21,22,12,02,01,11,10,

01,00,10,20,21,22,12,02,01,11,12,

01,00,10,20,21,22,12,02,01,11,21,

01,00,10,20,21,22,12,11,01,02,12,

using the reference:

a: 02,12 12,02
b: 12,22 22,12
c: 01,02 02,01
d: 11,12 12,11
e: 21,22 22,21
f: 01,11 11,01
g: 11,21 21,11
h: 00,01 01,00
i: 10,11 11,10
j: 20,21 21,20
k: 00,10 10,00
l: 10,20 20,10

DefDbl A-Z

Dim crlf$, seg(12) As String

Private Sub Form_Load()

Form1.Visible = True

Text1.Text = ""

crlf = Chr$(13) + Chr$(10)

Open "ten seg ref.txt" For Input As #1

For i = 1 To 12

Line Input #1, seg(i)

Close 1

Open "ten seg input.txt" For Input As #1

Line Input #1, l$

bld$ = ""

For i = 1 To 28 Step 3

lkup$ = Mid(l, i, 5)

For j = 1 To 12

If InStr(seg(j), lkup) > 0 Then Exit For

If j > 12 Then Text1.Text = Text1.Text & "error": Exit Sub

Text1.Text = Text1.Text & Left(seg(j), 1)

bld = bld & Left(seg(j), 1)

Text1.Text = Text1.Text & " "

For i = 1 To 12

If InStr(bld, Mid("abcdefghijkl", i, 1)) = 0 Then Text1.Text = Text1.Text & Mid("abcdefghijkl", i, 1)

Text1.Text = Text1.Text & crlf

Loop Until EOF(1)

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

End Sub

Posted by Charlie on 2016-02-19 14:09:29

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