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Half odd, half even (Posted on 2014-10-16) Difficulty: 3 of 5
How many distinct solutions are there to the alphametic
EO*OE=OEOE?

What if Itold you that the two partial products are:
OOO & EEE?

O & E stand for odd and even digits respectively.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution | Comment 2 of 3 |
DefDbl A-Z
Dim crlf$, used(9)

Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For a = 2 To 8 Step 2
 For b = 1 To 9 Step 2
 For c = 1 To 9 Step 2
 For d = 0 To 8 Step 2
   ab = 10 * a + b
   cd = 10 * c + d
   prod = ab * cd
   pr$ = LTrim(Str(prod))
   If InStr("13579", Mid(pr$, 1, 1)) > 0 Then
   If InStr("02468", Mid(pr$, 2, 1)) > 0 Then
   If InStr("13579", Mid(pr$, 3, 1)) > 0 Then
   If InStr("02468", Mid(pr$, 4, 1)) > 0 Then
      Text1.Text = Text1.Text & ab & Str(cd) & "   " & prod
      good = 1
      pp1$ = LTrim(Str(ab * d))
      pp2$ = LTrim(Str(ab * c))
      If Len(pp1) = 3 And Len(pp2) = 3 Then
        For i = 1 To 3
          If InStr("02468", Mid(pp1, i, 1)) > 0 Then Mid(pp1, i, 1) = "e" Else Mid(pp1, i, 1) = "o"
          If InStr("02468", Mid(pp2, i, 1)) > 0 Then Mid(pp2, i, 1) = "e" Else Mid(pp2, i, 1) = "o"
        Next
        If pp1 = "ooo" And pp2 = "eee" Or pp1 = "eee" And pp2 = "ooo" Then
          Text1.Text = Text1.Text & " * "
        End If
      End If
      pp1$ = LTrim(Str(cd * b))
      pp2$ = LTrim(Str(cd * a))
      If Len(pp1) = 3 And Len(pp2) = 3 Then
        For i = 1 To 3
          If InStr("02468", Mid(pp1, i, 1)) > 0 Then Mid(pp1, i, 1) = "e" Else Mid(pp1, i, 1) = "o"
          If InStr("02468", Mid(pp2, i, 1)) > 0 Then Mid(pp2, i, 1) = "e" Else Mid(pp2, i, 1) = "o"
        Next
        If pp1 = "ooo" And pp2 = "eee" Or pp1 = "eee" And pp2 = "ooo" Then
          Text1.Text = Text1.Text & " r "
        End If
      End If
      
      Text1.Text = Text1.Text & crlf
      ct = ct + 1
      DoEvents
   End If
   End If
   End If
   End If
 Next
 Next
 Next
 Next
 
 Text1.Text = Text1.Text & ct & crlf & "done"
End Sub

finds 65 distinct solutions:

EO OE   OEOE
21 50   1050
21 52   1092
21 58   1218
21 70   1470
21 78   1638
21 90   1890
23 70   1610
23 72   1656
25 50   1250
25 58   1450
25 74   1850
27 54   1458
27 70   1890
29 50   1450
41 30   1230
41 36   1476
41 74   3034
41 90   3690
41 94   3854
43 30   1290
43 38   1634
43 70   3010
43 72   3096
43 90   3870
47 30   1410
47 36   1692
47 70   3290
47 74   3478
49 30   1470
49 70   3430
61 18   1098
61 30   1830
61 50   3050
61 54   3294
61 56   3416
61 90   5490
61 92   5612
61 96   5856
63 30   1890
63 52   3276
63 58   3654
63 90   5670
65 50   3250
65 78   5070
65 90   5850
67 16   1072
67 54   3618 * 
67 76   5092
69 50   3450
81 16   1296
81 18   1458
81 38   3078
81 70   5670
81 72   5832
81 90   7290
81 92   7452
81 94   7614
83 18   1494
83 70   5810
83 90   7470
83 92   7636
85 38   3230
85 90   7650
87 14   1218
87 90   7830

The one marked with an asterisk is the only one that has the two given partial products.

  Posted by Charlie on 2014-10-16 15:07:00
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