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 Hi there, Pascal (Posted on 2014-09-01)
How many odd entries are there in the 2014th row of Pascal's Triangle?

Rem: Please compare with my "Bonjour, Pascal!" of April 2014 .

 See The Solution Submitted by Ady TZIDON No Rating

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 computer solution | Comment 1 of 2
DefDbl A-Z
Dim crlf\$, row(1, 3000)

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

row(1, 1) = 1: row(1, 2) = 1
For n = 2 To 2014
For i = 1 To n
row(0, i) = row(1, i)
Next
totodd = 0
For i = 1 To n + 1
row(1, i) = (row(0, i) + row(0, i - 1)) Mod 2

If row(1, i) Then totodd = totodd + 1
Next
Text1.Text = Text1.Text & Str(n) & Str(totodd) & crlf
DoEvents
Next

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

The first few rows show the following counts:

2 2 (1 2 1)
3 4 (1 3 3 1)
4 2 etc.
5 4
6 4
7 8
8 2
9 4
10 4
11 8
12 4
13 8
14 8
15 16
16 2
17 4
18 4
19 8
20 4
21 8
22 8
23 16
24 4
25 8
26 8
27 16
28 8
29 16
30 16
31 32
32 2
33 4
34 4
35 8
36 4
37 8
38 8
39 16
40 4
41 8
42 8

Then at the end:

2001 128
2002 128
2003 256
2004 128
2005 256
2006 256
2007 512
2008 128
2009 256
2010 256
2011 512
2012 256
2013 512
2014 512

So the 2014th row has 512 odd numbers.

Also, BTW, one does see the pattern for Bonjour, Pascal.

 Posted by Charlie on 2014-09-01 12:36:58

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