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Oddly even numbers (Posted on 2017-10-01) Difficulty: 3 of 5
Let an oddly even number be an even number that contains its greatest odd factor. For example, 1792=2^8*7 is an oddly even number because the greatest odd factor of 1792 is 7, which is in 1792. X and Y are both oddly even numbers. When you remove the first digit of X, you get Y. What are X and Y?

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Solution computer solution Comment 1 of 1
The first 63 oddly even numbers (all those below 2 million) are listed below together with their greatest odd factors:

 16 1
 128 1
 384 3
 512 1
 1024 1
 1536 3
 1792 7
 2176 17
 2560 5
 2912 91
 3072 3
 5120 5
 7168 7
 8192 1
 9216 9
 11264 11
 13312 13
 15360 15
 15616 61
 16384 1
 17408 17
 19456 19
 21504 21
 23552 23
 25600 25
 27648 27
 28672 7
 29696 29
 31744 31
 33792 33
 35840 35
 37376 73
 37888 37
 39936 39
 41984 41
 43392 339
 57344 7
 66560 65
 90112 11
 98304 3
 131072 1
 161792 79
 229376 7
 262144 1
 270336 33
 290912 9091
 294912 9
 393216 3
 397312 97
 443392 433
 458752 7
 491520 15
 497152 971
 589824 9
 655360 5
 786432 3
 917504 7
 1048576 1
 1179648 9
 1185792 579
 1323008 323
 1474560 45
 1955840 955
 
The two that fit the puzzle's description of X and Y are: 

443392 and 43392

from:

DefDbl A-Z
Dim crlf$
Dim fct(20, 1), oddlyEven$(1000)


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For n = 2 To 2000000 Step 2
    gof = n
    While gof Mod 2 = 0
       gof = gof / 2
    Wend
    g$ = LTrim(Str(gof))
    ns$ = LTrim(Str(n))
    If InStr(ns$, g) > 0 Then
      Text1.Text = Text1.Text & Str(ns) & Str(g) & crlf
      ct = ct + 1
      oddlyEven(ct) = ns
    End If
    
    DoEvents
 Next
 Text1.Text = Text1.Text & crlf
 
 For i = 1 To ct
  For j = 1 To i - 1
     If oddlyEven(j) = Mid(oddlyEven(i), 2) Then
       Text1.Text = Text1.Text & oddlyEven(i) & "  " & oddlyEven(j) & crlf
     End If
  Next
Next
 
 
 Text1.Text = Text1.Text & crlf & ct & " done"
  
End Sub

Edited on October 1, 2017, 3:50 pm
  Posted by Charlie on 2017-10-01 15:48:18

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