# Antimail

Adi Oltean's Weblog - Flashbacks on technology, programming, and other interesting things

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• #### Blog Post: 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: ChessBase ]
• #### Blog Post: 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 sense, information theory, etc. But surprisingly...
• #### Blog Post: 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 called the “vortessence”. One interesting property...
• #### Blog Post: 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 in to the flight and promptly realizes that he...
• #### Blog Post: Puzzle: prime numbers

Show that (N^4 + 4^N) is a prime number if and only if N=1.
• #### Blog Post: 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 is either black or white]
• #### Blog Post: 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 and set it to TRUE. What is the average number...
• #### Blog Post: 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?
• #### Blog Post: 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 the same color as itself, so the propery...

• #### Blog Post: 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 solution becomes trivial. We will perform the...
• #### Blog Post: 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 as you can see :-) And now, a real math...
• #### Blog Post: 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 that is waiting for them on the ground, is killed...
• #### Blog Post: 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 one cube will contain "1" and another face on the...
• #### Blog Post: 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 be in isolated cells and will have no communication...
• #### Blog Post: Puzzle: what is the next card?

This is a very nice puzzle that kept me awake for a long time... :-) John and Dianne, two journalists (and experienced bridge players), are captured by some foreign government. The guardian says that he can free them, if they win the following game. First, Dianne must choose five random cards from...

This problem initially had two parts but now has three. OK, let's start with this: let's assume that we have two, trains, 100 miles apart, each going with 20 mph to the other. A fly travels between them at 50 mph, zig-zagging just before getting smashed between the trains. Question: How far does the...
• #### Blog Post: Puzzle: do you know chemistry?

Here is a very nice puzzle - But unfortunately you have to ressurect a little chemistry knowledge to fully appreciate it... You have two identical test tubes. Both tubes look identical - they both contain colourless, odoreless, aqueous solutions. But someone told you that one of them contains a solution...
• #### Blog Post: Puzzle: geometry problem

Here is a fun one: The triangle ABC is isoseceles, with angle (ABC) = angle (ACB) = 80°. We draw now two segments inside the triangle. First, we choose the point D on segment AC such that angle (CBD) is 60°. Also, we choose the point E on AB, where angle (BCE) is 50°. We now extend DE until it intersects...
• #### Blog Post: Puzzle: How many witches are there?

It is known that in a certain city there are a significant number of witches, even though this practice is forbidden. The problem is that nobody knows who these witches are, since a witch is very careful to appear to others as a perfectly normal person. You are appointed by the Mayor to establish (as...
• #### Blog Post: Puzzle: solve this equation!

You have the following false "equation", made with six toothpicks arranged on a table in the following way: XI = I You have to re-establish the equality by changing the position of a single toothpick. Common-sense rules apply: you are not allowed to bend, break, or remove any toothpicks.
• #### Blog Post: Quick Puzzle: what does this program print?

You have 30 seconds left... just kidding :-) using System; using System.Collections; using System.Reflection; class Hello { Type Unknown { get { return World.GetType(); } } object [] Knowledge() { return Unknown.GetProperties(); } string [] Library() { return Array .ConvertAll< object , string >...
• #### Blog Post: Script puzzle: Solving Hanoi ... in shell

If you like CMD programming, here is a challenge for you: write a CMD batch file that solves the Hanoi problem. You start with these folders: and you must end up with this state: You probably know the rules of the Hanoi problem. Mapped in the command shell terminology these rules are as follows: 1) You...
• #### Blog Post: Another puzzle: Gödel, Goldbach and other "G" names...

Mr Blobby posted an excellent comment in my previous post, outlining in a few words Gödel's proof of incompleteness of arithmetics. This is a mind-boggling result, which essentially states the following: There are certain statements (I would not say "theorems") in the body of Arithmetics, which are either...
• #### Blog Post: Puzzle: Shakespeare numbers...

Imagine that there might be a real number that contains (in an encoded form) the entire works of Shakespeare. Let's call this number a "Shakespeare number". Can you give an example of an algorithm to generate Shakespeare numbers? [update] The problem, as originally stated, is too vague. I added more...
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