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 Squares on Cubes (Posted on 2008-04-30)
I applied one of the digits 1 through 9 to each cell of the provided net of a cube.
My object was to create a unique 4 digit square number on each face. At the same time I required each vertex to be a 3 digit square. I failed in that objective!
I have 6 unique 4 digit squares but I have duplicated just one of my vertices.

To emulate my "feat":
- a [Magenta] Magenta cell is both the first digit of a 3 and 4 digit square
- an [Orange] Orange cell signifies the first digit of only a 4 digit square, while
- a [Cyan] Cyan cell signifies the first cell only of a 3 digit square.

The digits must be applied to each face by rotation, the direction is defined by need. "A" through "F" represent the 6 faces of the cube while "a" through "h" represent the vertices of the cube when fully assembled.
Note: Within the range allowed several squares utilise the same digits, and this is allowed by virtue of the commencement cell.
But then, there is still the challenge for 6 unique faces and 8 unique vertices.

 See The Solution Submitted by brianjn Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: better classification of results | Comment 17 of 21 |
(In reply to better classification of results by Charlie)

For those interested in the program used to produce the better classification:

Dim sqr4(200), sqr3(100), had4(200), ctSol, numSqr3, vCt(100)
Private Sub cmdStart_Click()
Open "squares on cube 7 diff.txt" For Output As #2
Open "squares on cube 8 diff.txt" For Output As #3
Open "squares on cube other diff.txt" For Output As #4
FontTransparent = False
For i = 100 To 999
sr = Int(Sqr(i) + 0.5)
If sr * sr = i Then
s = LTrim(Str(i))
If InStr(s, "0") = 0 Then
numSqr3 = numSqr3 + 1
sqr3(numSqr3) = s
Print s; " ";
End If
End If
Next
Print: Print numSqr3: Print
For i = 1000 To 9999
sr = Int(Sqr(i) + 0.5)
If sr * sr = i Then
s = LTrim(Str(i))
If InStr(s, "0") = 0 Then
numSqr4 = numSqr4 + 1
sqr4(numSqr4) = LTrim(Str(i))
Print s; " ";
End If
End If
Next
Print: Print numSqr4: Print
DoEvents

For A = 1 To numSqr4
CurrentX = 1: CurrentY = TextHeight("X") * 12
Print A; numSqr4; ctSol: DoEvents
Aa = Left(sqr4(A), 1)
For dirA = 1 To 2
If dirA = 1 Then
Ae = Mid(sqr4(A), 2, 1)
Af = Mid(sqr4(A), 3, 1)
Ab = Mid(sqr4(A), 4, 1)
Else
Ab = Mid(sqr4(A), 2, 1)
Af = Mid(sqr4(A), 3, 1)
Ae = Mid(sqr4(A), 4, 1)
End If
For va = 1 To numSqr3
vCt(va) = vCt(va) + 1
For dirVa = 1 To 2
goodVa = True
If Mid(sqr3(va), 2, 1) = Aa And dirVa = 1 Then
Ba = Left(sqr3(va), 1): Ca = Right(sqr3(va), 1)
ElseIf Mid(sqr3(va), 3, 1) = Aa And dirVa = 2 Then
Ba = Left(sqr3(va), 1): Ca = Mid(sqr3(va), 2, 1)
Else
goodVa = False
End If
If goodVa Then
For B = 1 To numSqr4
For dirB = 1 To 2
goodB = True
If dirB = 1 And Mid(sqr4(B), 4, 1) = Ba Then
Bd = Left(sqr4(B), 1)
Bh = Mid(sqr4(B), 2, 1)
Be = Mid(sqr4(B), 3, 1)
ElseIf dirB = 2 And Mid(sqr4(B), 2, 1) = Ba Then
Bd = Left(sqr4(B), 1)
Bh = Mid(sqr4(B), 4, 1)
Be = Mid(sqr4(B), 3, 1)
Else
goodB = False
End If
If goodB Then
For vd = 1 To numSqr3
vCt(vd) = vCt(vd) + 1
If Left(sqr3(vd), 1) = Bd Then
For dirVd = 1 To 2
If dirVd = 1 Then
Cd = Mid(sqr3(vd), 2, 1)
Fd = Mid(sqr3(vd), 3, 1)
Else
Fd = Mid(sqr3(vd), 2, 1)
Cd = Mid(sqr3(vd), 3, 1)
End If
For C = 1 To numSqr4
If Left(sqr4(C), 1) = Cd Then
For dirC = 1 To 2
goodC = True
If dirC = 1 And Mid(sqr4(C), 2, 1) = Ca Then
Cb = Mid(sqr4(C), 3, 1)
Cc = Mid(sqr4(C), 4, 1)
ElseIf dirC = 2 And Mid(sqr4(C), 4, 1) = Ca Then
Cb = Mid(sqr4(C), 3, 1)
Cc = Mid(sqr4(C), 2, 1)
Else
goodC = False
End If
If goodC Then
For vertb = 1 To numSqr3
vCt(vertb) = vCt(vertb) + 1
For dirVb = 1 To 2
If dirVb = 1 And Mid(sqr3(vertb), 2, 2) = (Cb & Ab) Or dirVb = 2 And Mid(sqr3(vertb), 2, 2) = Ab & Cb Then
Db = Left(sqr3(vertb), 1)
For D = 1 To numSqr4
If Left(sqr4(D), 1) = Db And had4(D) = False Then
For dirD = 1 To 2
If dirD = 1 Then
Df = Mid(sqr4(D), 2, 1)
Dg = Mid(sqr4(D), 3, 1)
Dc = Mid(sqr4(D), 4, 1)
ElseIf dirD = 2 Then
Df = Mid(sqr4(D), 4, 1)
Dg = Mid(sqr4(D), 3, 1)
Dc = Mid(sqr4(D), 2, 1)
End If
For vc = 1 To numSqr3
vCt(vc) = vCt(vc) + 1
For dirVc = 1 To 2
If dirVc = 1 And Mid(sqr3(vc), 2, 2) = (Cc & Dc) Or dirVc = 2 And Mid(sqr3(vc), 2, 2) = Dc & Cc Then
Fc = Left(sqr3(vc), 1)

For F = 1 To numSqr4
If Fc = Left(sqr4(F), 1) And had4(F) = False Then
For dirF = 1 To 2
goodF = True
If dirF = 1 And Fd = Mid(sqr4(F), 4, 1) Then
Fg = Mid(sqr4(F), 2, 1)
Fh = Mid(sqr4(F), 3, 1)
ElseIf dirF = 2 And Fd = Mid(sqr4(F), 2, 1) Then
Fg = Mid(sqr4(F), 4, 1)
Fh = Mid(sqr4(F), 3, 1)
Else
goodF = False
End If
If goodF Then

For vh = 1 To numSqr3
vCt(vh) = vCt(vh) + 1
If Fh = Left(sqr3(vh), 1) Then
For dirVh = 1 To 2
goodVh = True
If dirVh = 1 And Mid(sqr3(vh), 3, 1) = Bh Then
Eh = Mid(sqr3(vh), 2, 1)
ElseIf dirVh = 2 And Mid(sqr3(vh), 2, 1) = Bh Then
Eh = Mid(sqr3(vh), 3, 1)
Else
goodVh = False
End If
If goodVh Then

For vg = 1 To numSqr3
vCt(vg) = vCt(vg) + 1
If Fg = Left(sqr3(vg), 1) Then
For dirVg = 1 To 2
goodVg = True
If dirVg = 1 And Mid(sqr3(vg), 2, 1) = Dg Then
Eg = Mid(sqr3(vg), 3, 1)
ElseIf dirVg = 2 And Mid(sqr3(vg), 3, 1) = Dg Then
Eg = Mid(sqr3(vg), 2, 1)
Else
goodVg = False
End If
If goodVg Then

For E = 1 To numSqr4
If Left(sqr4(E), 1) = Eg And had4(E) = False Then
For dirE = 1 To 2
goodE = True
If dirE = 1 And Eh = Mid(sqr4(E), 4, 1) Then
Ef = Mid(sqr4(E), 2, 1)
Ee = Mid(sqr4(E), 3, 1)
ElseIf dirE = 2 And Eh = Mid(sqr4(E), 2, 1) Then
Ee = Mid(sqr4(E), 3, 1)
Ef = Mid(sqr4(E), 4, 1)
Else
goodE = False
End If ' new4 E
If goodE Then
'             chw = TextWidth("W"): chh = TextHeight("W")
'             CurrentX = 4 * chw: CurrentY = 13 * chh
'             Print Ae; "   "; Af
'             CurrentX = 4 * chw: CurrentY = 15 * chh
'             Print Aa; "   "; Ab
'             CurrentX = 1 * chw: CurrentY = 17 * chh
'             Print Be; "   "; Ba; "   "; Ca; "   "; Cb; "   "; Db; "   "; Df; "   "; Ef; "   "; Ee
'             CurrentX = 1 * chw: CurrentY = 19 * chh
'             Print Bh; "   "; Bd; "   "; Cd; "   "; Cc; "   "; Dc; "   "; Dg; "   "; Eg; "   "; Eh
'             CurrentX = 4 * chw: CurrentY = 21 * chh
'             Print Fd; "   "; Fc
'             CurrentX = 4 * chw: CurrentY = 23 * chh
'             Print Fh; "   "; Fg
DoEvents
ctB = ctB + 1
tr1 = Ef & Df & Af
tr2 = Ef & Af & Df
tr3 = Ee & Ae & Be
tr4 = Ee & Be & Ae

If onList(tr1) And onList(tr3) Then
For ix = 1 To numSqr3
If sqr3(ix) = tr1 Then vf = ix
If sqr3(ix) = tr3 Then ve = ix
Next
GoSub reportIt
End If
If onList(tr1) And onList(tr4) Then
For ix = 1 To numSqr3
If sqr3(ix) = tr1 Then vf = ix
If sqr3(ix) = tr4 Then ve = ix
Next
GoSub reportIt
End If
If onList(tr2) And onList(tr3) Then
For ix = 1 To numSqr3
If sqr3(ix) = tr2 Then vf = ix
If sqr3(ix) = tr3 Then ve = ix
Next
GoSub reportIt
End If
If onList(tr2) And onList(tr4) Then
For ix = 1 To numSqr3
If sqr3(ix) = tr2 Then vf = ix
If sqr3(ix) = tr4 Then ve = ix
Next
GoSub reportIt
End If

End If ' goodE
Next dirE
End If ' Eg matches
Next E

End If ' goodVg
Next dirVg
End If ' Fg is first digit of vg
vCt(vg) = vCt(vg) - 1
Next vg

End If ' goodVh
Next dirVh
End If ' Fh is first digit of vh
vCt(vh) = vCt(vh) - 1
Next vh

End If ' goodF
Next dirF
End If ' Fc matches
Next F

End If ' good dirVc
Next dirVc
vCt(vc) = vCt(vc) - 1
Next vc
Next dirD
End If ' D begins with Db
Next D
End If ' good vertb
Next dirVb
vCt(vertb) = vCt(vertb) - 1
Next vertb
End If ' goodC
Next dirC
End If ' C fits Cd
Next C
Next
End If ' sqr3(vd) begins with Bd
vCt(vd) = vCt(vd) - 1
Next vd
End If ' goodB
Next dirB
Next B
End If ' goodVa
Next dirVa
vCt(va) = vCt(va) - 1

Next va
Next dirA
Next A
Print "end"; ctSol
Close
Exit Sub

reportIt:
vCt(vf) = vCt(vf) + 1
vCt(ve) = vCt(ve) + 1

nCtTot = 0
For ix = 1 To numSqr3
If vCt(ix) > 0 Then nCtTot = nCtTot + 1
Next
If nCtTot = 7 Then
fNo = 2
ElseIf nCtTot = 8 Then
fNo = 3
Else
fNo = 4
End If

Print #fNo, "   "; Ae; Af
Print #fNo, "   "; Aa; Ab
Print #fNo, Be; Ba; " "; Ca; Cb; " "; Db; Df; " "; Ef; Ee
Print #fNo, Bh; Bd; " "; Cd; Cc; " "; Dc; Dg; " "; Eg; Eh
Print #fNo, "   "; Fd; Fc
Print #fNo, "   "; Fh; Fg
Print #fNo, sqr4(A); " "; sqr4(B); " "; sqr4(C); " "; sqr4(D); " "; sqr4(E); " "; sqr4(F)
Print #fNo, sqr3(va); " "; sqr3(vertb); " "; sqr3(vc); " "; sqr3(vd); " "; sqr3(ve); " "; sqr3(vf); " "; sqr3(vg); " "; sqr3(vh)
For iCtr = 1 To numSqr3
If vCt(iCtr) > 0 Then
Print #fNo, sqr3(iCtr); vCt(iCtr); "   ";
End If
Next
Print #fNo,: Print #fNo,: Print #fNo,
ctSol = ctSol + 1
vCt(vf) = vCt(vf) - 1
vCt(ve) = vCt(ve) - 1
Return
End Sub
Function onList(s)
For i = 1 To numSqr3
If s = sqr3(i) Then onList = True: Exit Function
Next
onList = False
End Function

 Posted by Charlie on 2008-05-03 10:05:25

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