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Odd partition (Posted on 2019-05-09) Difficulty: 3 of 5
There are 3 ways to write 4 as a sum of odd numbers (assuming order matters and numbers can be repeated in the sum): 3+1, 1+3, and 1+1+1+1.

How many ways are there to write 19 as a sum of odd numbers?

Hint: The above result has something to do with Fibonacci numbers

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf$, ways, n, togo



Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For n = 2 To 25
   ways = 0
   togo = n
   addon
   Text1.Text = Text1.Text & n & Str(ways) & crlf
 Next
 
  
  
  
 Text1.Text = Text1.Text & ct & " done"
End Sub

Sub addon()
  For amt = 1 To togo Step 2
    togo = togo - amt
    If togo = 0 Then
      ways = ways + 1
    Else
      addon
    End If
    togo = togo + amt
  Next
End Sub

finds

2 1
 3     2
 4     3
 5     5
 6    8
 7   13
 8   21
 9   34
10  55
11  89
12 144
13 233
14 377
15 610
16 987
17 1597
18 2584
19 4181
20 6765
21 10946
22 17711
23 28657
24 46368
25 75025

For 19, the sum is 4181. I do see the Fibonacci sequence here.

  Posted by Charlie on 2019-05-09 14:13:14
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