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]


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, it does have a solution….


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 of voting through…


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…


Puzzle: prime numbers

Show that (N^4 + 4^N) is a prime number if and only if N=1.


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]…


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 of elements…


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?


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 is…


Two math puzzles

What is the value of this expression? If that was too easy, how about this one?