All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Table's peculiarity (Posted on 2015-11-29) Difficulty: 3 of 5
Prove that no matter how each cell of a 5 x 41 table is filled with a 0 or 1, one can choose 3 rows and 3 columns which intersect in 9 cells filled with identical numbers.

Prove that 41 is the lowest possible n for 5 x n table; i.e., the statement is not true for a 5 x 40 table.

Source: Colorado math contest.

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Example needed | Comment 3 of 6 |
(In reply to Example needed by broll)

first example below: rows 1, 15 and 29; columns 1, 2 and 4:
 0 0 1 0 1
 0 0 1 0 1
 0 0 1 0 1

those columns in those rows are all zeros

likewise for the other sets listed below

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

DefDbl A-Z
Dim crlf$, grid(41, 5)


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 Open "tables peculiarity.txt" For Input As #1
 For i = 1 To 41
   Line Input #1, s$
   For p = 2 To 10 Step 2
     grid(i, p / 2) = Val(Mid(s, p, 1))
   Next
 Next
 Close
 
 For r1 = 1 To 39
 For r2 = r1 + 1 To 40
 For r3 = r2 + 1 To 41
 For c1 = 1 To 3
 For c2 = c1 + 1 To 4
 For c3 = c2 + 1 To 5
   DoEvents
   If grid(r1, c2) = grid(r1, c1) Then
   If grid(r1, c3) = grid(r1, c1) Then
   If grid(r2, c1) = grid(r1, c1) Then
   If grid(r2, c2) = grid(r1, c1) Then
   If grid(r2, c3) = grid(r1, c1) Then
   If grid(r3, c1) = grid(r1, c1) Then
   If grid(r3, c2) = grid(r1, c1) Then
   If grid(r3, c3) = grid(r1, c1) Then
     Text1.Text = Text1.Text & r1 & Str(r2) & Str(r3) & "    " & Str(c1) & Str(c2) & Str(c3) & crlf
   End If
   End If
   End If
   End If
   End If
   End If
   End If
   End If
 Next
 Next
 Next
 Next
 Next
 Next

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


  Posted by Charlie on 2015-11-30 08:24:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (10)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information