Puzzles Puzzles Puzzles

Want a real challenge? Tired of silly puzzle books with ridiculously easy problems? Then try these.

Well, this is my puzzle section, dedicated to challenging the world with puzzles which are tough as nuts! Don't worry if you end up tearing your hair to bits or are unable to sleep for the next few nights because of these problems. It's a natural thing.

Puzzle 1: (13 Oct 97)

Prepare to meet my notorious equation, one that has been solved by none save me. Took me 6 seconds to come up with the equation and 6 months to solve it. Heck, I was only 9 at that time. Let's see if you can beat that.

Solve for X, Y and Z such that X^Y + Y^Z = Z^X excluding trivial solutions. They need not be integer solutions.

Note: I have only established solutions for X, Y and Z in the real domain. As for the non-real domain, I have no answers, but feel free to contribute. Any answers other than my own will be posted in the answers page, along with the submitter's name, so here's your chance to fame and glory.

Puzzle 2: (25 July 1998)

This is an interesting problem from a Russian mathematics competition, the name and date of which I cannot remember.

Place 6 points on a plane surface such that any 3 points form the vertices of an isosceles triangle.

Puzzle 3: (25 July 1998)

You may have come across this before, but unlike most others, I'm not asking for just one solution, I'm asking for all 12! Here goes:

Find all 12 distinct ways to place 8 chess queens on a chessboard such that no two queens are attacking each other.

Give up yet? Take a peek at the solutions.