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Puzzles (RSS)

Puzzle: create a Pentagon with rule and compass <EOM>

The title sums it all.   P.S. And, as a Christmas bonus, here is a nice chess puzzle. In the above diagram you must add the two missing kings in such a way that White, who is on the move, can deliver immediate mate, i.e. mate in one move. [source: Read More...
Posted Wednesday, December 26, 2007 11:37 PM by AdiOltean | 9 Comments
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Puzzle solution: Xen voting algorithm

I think that the problem stated in one of my earlier posts is one of the most fascinating puzzles I came across recently. Many people that got confronted with it said bluntly that the problem simply has no solution, otherwise it would contradict common Read More...
Posted Monday, November 26, 2007 1:19 PM by AdiOltean | 3 Comments
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Puzzle: Xen voting algorithm

There is a huge amount of aliens living on the Xen planet who want to elect their new leader (since their previous leader died a while back). They want to switch to a very democratic voting process, through the help of a very special communication field Read More...
Posted Monday, October 29, 2007 9:52 PM by AdiOltean | 8 Comments
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Simple probability problem

I love probability puzzles. Here is one I liked: There are a 100 people trying to get onto the same flight you are. The airplane has a 100 seats. You are all ready to board. You are the last one in the line of passengers at the gate. The first guy walks Read More...
Posted Friday, August 18, 2006 11:20 PM by AdiOltean | 32 Comments
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Puzzle: prime numbers

Show that (N^4 + 4^N) is a prime number if and only if N=1. Read More...
Posted Tuesday, March 07, 2006 8:20 PM by AdiOltean | 9 Comments
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Puzzle: another probability problem

If you have an urn who already contains either a black or white ball, and you add a white ball to it, and then you subtract a white ball from it, then what is the probability of having a white ball left? [update: adding the fact that the original ball Read More...
Posted Tuesday, January 10, 2006 6:45 PM by AdiOltean | 11 Comments
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Puzzle: probability problem

Here is an interesting probability problem who recently generated long discussions in our team: Say that you have an array of N boolean values, with all values initially set to FALSE. At each iteration step, you arbitrary pick an element in the array Read More...
Posted Wednesday, December 28, 2005 1:56 PM by AdiOltean | 6 Comments
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Math puzzle: minimum number?

What is the minimum number that cannot be expressed with less than two english words? Also, how about less than thirteen english words? Read More...
Posted Tuesday, November 29, 2005 9:02 PM by AdiOltean | 13 Comments
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Puzzle: all horses have the same color

Several answers to my previous puzzle reminded me about an old result: Theorem: All horses have the same color. Proof : We demonstrate this by induction over N for all the sets of horses size of size N: - N=1: The proof is true for N = 1 (any horse has Read More...
Posted Tuesday, September 13, 2005 5:55 PM by AdiOltean | 5 Comments
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Two math puzzles

What is the value of this expression? If that was too easy, how about this one? Read More...
Posted Monday, September 12, 2005 3:10 PM by AdiOltean | 22 Comments
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Puzzle Solution: a geometry problem

The geometry problem from my previous math puzzle has a nice solution. I particularly like it because it is one of these problems that are pretty hard to solve traditionally - unless you perform the right geometric construction - and at that point, the Read More...
Posted Thursday, August 18, 2005 8:35 PM by AdiOltean | 4 Comments
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Puzzle: a little geometry problem, and a sequence question

This is not really a puzzle, but a real geometry problem. Let's take a random triangle (ABC), and let's assume that the angle bisector from A intersects BC in the point D. Proof that: AD ^ 2 = AB * AC - BD * CD Here is the figure, drawn in MSPAINT.EXE Read More...
Posted Saturday, August 06, 2005 12:44 AM by AdiOltean | 15 Comments
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Puzzle: When everything goes wrong

During war, two spies (Jack and Arnold) are being parachuted in a hostile country. But during their landing, their plane gets intercepted by the special forces. Things started to go out of control: they both lose all their equipment, and Ann, the person Read More...
Posted Friday, July 01, 2005 3:30 PM by AdiOltean | 10 Comments
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Puzzle: two cubes

You are given two white cubes. You are asked to draw a digit (from 0..9) on every square of these cubes, such that you will be able to represent evert day in a month using these cubes in certain position. For example, "13" would require that a face on Read More...
Posted Monday, June 27, 2005 5:24 PM by AdiOltean | 6 Comments
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Puzzle: How do you get out of the prison (Part II)

The previous puzzle was solved correctly in the comments. So I thought to present with another prison-style puzzle: A warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will Read More...
Posted Friday, June 24, 2005 11:09 PM by AdiOltean | 7 Comments
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