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Search: Posts Made By: Kees
Forum: Lounge 2009-08-31, 07:48
Replies: 28
Views: 1,784
Posted By Kees
V-E+F=2

V-E+F=2
Forum: Puzzles 2009-05-07, 15:24
Replies: 16
Views: 969
Posted By Kees
One example for 7 lines on a 8x8 square: 7 1...

One example for 7 lines on a 8x8 square:

7 1 1 2 2 3 4 4
7 1 2 2 3 3 4 5
1 1 2 3 3 4 4 5
1 2 2 3 4 4 5 5
1 2 3 3 4 5 5 6
2 2 3 4 4 5 6 6
2 3 3 4 5 5 6 7
2 3 4 4 5 6 6 7
Forum: Puzzles 2009-05-05, 16:15
Replies: 16
Views: 969
Posted By Kees
Lines in a Square

Consider an n x n chessboard.
What is the size of the smallest collection of lines such that every square of the chessboard is intersected by at least one line ?

PS: I do not pretend to have a...
Forum: Puzzles 2009-04-27, 15:49
Replies: 33
Views: 1,699
Posted By Kees
http://arxiv.org/abs/0904.1757

http://arxiv.org/abs/0904.1757
Forum: Puzzles 2009-04-24, 15:09
Replies: 33
Views: 1,699
Posted By Kees
Start with small dimension (n=3, n=4) For...

Start with small dimension (n=3, n=4)

For n=3 we get a resistance of

1/3 + 1/6 + 1/3 = 5/6

For n=4 we get a resistance of

1/4 + 1/12 + 1/12 + 1/4= 2/3
Forum: Puzzles 2009-01-26, 10:46
Replies: 22
Views: 1,122
Posted By Kees
8/(3-8/3)=24

8/(3-8/3)=24
Forum: Soap Box 2008-12-16, 09:48
Replies: 820
Views: 39,724
Posted By Kees
As to cats on laptops... ...

As to cats on laptops...

http://www.catswhothrowupgrass.com/kill.php

:cat:
Forum: Math 2008-11-07, 14:29
Replies: 3
Views: 478
Posted By Kees
Obviously, we can write \prod_{1\le j<i\le...

Obviously, we can write
\prod_{1\le j<i\le n}(i-j)=\prod_{i=1}^n (i-1)!
I used the pigeonhole approach to prove the result for small n. But even for small n, you cannot use this method in a...
Forum: Math 2008-11-07, 12:11
Replies: 3
Views: 478
Posted By Kees
Looking for an elementary demonstration

a_1,\ldots,a_n
are integers, all different. It is possible to prove that
\prod_{i< j}(i-j) |\prod_{i<j}(a_i - a_j).
Either by using some techniques with Vandermonde Determinants or by proving a...
Forum: Lounge 2008-05-27, 12:26
Replies: 5
Views: 626
Posted By Kees
Cool Well, memorable or not, he signs his messages as...

Well, memorable or not, he signs his messages as Jacob...
Forum: PrimeNet 2008-05-07, 12:22
Replies: 311
Views: 16,422
Posted By Kees
I miss the old stats page too

I miss the old stats page too
Forum: Lounge 2008-03-27, 09:15
Replies: 75
Views: 3,015
Posted By Kees
Strasbourg, France

Strasbourg, France
Forum: Puzzles 2008-03-20, 11:32
Replies: 20
Views: 863
Posted By Kees
http://www.scanraid.com/sudoku.htm

http://www.scanraid.com/sudoku.htm
Forum: Math 2008-03-06, 09:58
Replies: 15
Views: 1,412
Posted By Kees
well, 43 obviously which makes it very...

well, 43 obviously

which makes it very uninteresting indeed
Forum: Math 2008-03-06, 09:14
Replies: 15
Views: 1,412
Posted By Kees
Talking I thought it was 37

I thought it was 37
Forum: Puzzles 2008-02-13, 15:47
Replies: 23
Views: 1,007
Posted By Kees
An interesting link, slightly related ...

An interesting link, slightly related

http://www.maa.org/mathland/mathland_5_19.html
Forum: Puzzles 2008-01-29, 09:29
Replies: 54
Views: 1,876
Posted By Kees
So for coordinate users: White: Ke1, c4 ...

So for coordinate users:

White: Ke1, c4
Black: Ke8

Is this the problem you have in mind ?
Forum: Chess 2008-01-18, 12:16
Replies: 42
Views: 2,329
Posted By Kees
Chess loses a legend

Bobby Fischer has passed away
Forum: Lounge 2007-11-26, 10:43
Replies: 289
Views: 11,089
Posted By Kees
I seem to remmeebr a smilair seeht but the frist...

I seem to remmeebr a smilair seeht but the frist and the lsat lteter raeimned in the smae pcale
Forum: Puzzles 2007-11-14, 07:23
Replies: 14
Views: 760
Posted By Kees
I get to 35 too as upperbound but I would be...

I get to 35 too as upperbound but I would be surprised if there were a configuration where 35 moves are actually needed
Forum: Puzzles 2007-11-13, 16:01
Replies: 14
Views: 760
Posted By Kees
1) numbers are randomly placed 2) exchange...

1) numbers are randomly placed
2) exchange between any two numbers is possible, not just adjacently placed numbers
3) final result applies to adjacent numbers
Forum: Puzzles 2007-11-13, 15:22
Replies: 14
Views: 760
Posted By Kees
Composite checkerboard

The numbers 1,2,...,100 are written in cells of a table 10 x 10, each number is written once. By one move, we may interchange numbers in any two cells.
After how many moves may we get a table, in...
Forum: Homework Help 2007-11-12, 14:12
Replies: 10
Views: 813
Posted By Kees
actually, I am not sure whether it would fall...

actually, I am not sure whether it would fall under rule 3 "overt answer".
Would "overt" mean that when the response given is handed in as homework answer, the homeworkee receives at least 80 % of...
Forum: Homework Help 2007-11-12, 14:07
Replies: 10
Views: 813
Posted By Kees
sorry, could not hide with TeX

sorry, could not hide with TeX
Forum: Homework Help 2007-11-12, 13:35
Replies: 10
Views: 813
Posted By Kees
A_{n+1}=A_n-\frac{1}{n+1}+\frac{1}{2n+1}+\frac{1}{...

A_{n+1}=A_n-\frac{1}{n+1}+\frac{1}{2n+1}+\frac{1}{2n+2}\\
=A_n+\frac{1}{2n+1}-\frac{1}{2n+2}=\\
\sum_{i=1}^{n+1}\frac{(-1)^{i+1}}{i}\\
\lim_{n\rightarrow\infty}A_n=\log 2

with the last by...
Showing results 1 to 25 of 196

 
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