No.1 :

The Swimming Duck's

After a long, troublesome flight in the south-west of china four tiny duck's arrive at a solitary monastery with two ponds.
The first pond is quadratic (6.1 x 6.1 m), the other one is circular with a diameter of  7 meters. Because the ducks are already very tired they decide to have a little rest, two ducks in each of the pools.

Observing this during his evening-meditation, the old monk Bun Li asks his best disciple the following problem: "Now, see these tiny ducks in our pools, Grasshopper, two in each of them. Randomly (uniformly distributed) they move along on the water. Well, what do you think in which of the two different-shaped ponds the ducks are nearer to each other (on an average) while they are swimming ???"

"But master", answeres the surprised Fu Jin, "the two ponds haven't equal size !"
"Yes, Grasshopper, a little bit greater is the circle in his harmony, and smaller is the other, but far-reaching are his edges !"

Now, what do YOU think was the exact mathematical answer from Fu Jin, satisfying his great master ???

Solution_1

No.2 : Just Puzzling ™



A few days ago little Billy got an easy 16 pieces-puzzle (4x4) for his fourth birthday. He was very happy about the lovely colorful parts, and when he already had put together some of the wonderful red, blue and green arrows, suddenly no other pieses matched to an arrows-pattern ! - He almost started to cry, but i hope, YOU can help him solve the puzzle, since there are only 16 pieces !...

Have Fun !




P.S.: One should not be afraid of the 2,246 * 10^22 possibilities to form a 4x4-square, althought there exists only ONE correct solution ! (for simplification without border-constraints)
Even if one could try 1.000.000 possibilities per second it would still take 700 million(!) years for all...
So, there will only help some logic & *combination* !

As anyone could solve the puzzle yet before Y3k, please send an e-mail for honoration...
Solution_2

*** NEW *** ...and another simple, but even better version you can find here (3² + 4² = 5²) .
(was published in Mensa-Austria-Magazin TopIQ , but no one could solve it, hehe;-)



No.3 : Three hikers in the triangle




Hiker-1 goes from Point A to Point B,
H-2 from B to C, H-3 : C -> A.
But all three hikers take a roundabout-route via the "Roundabout-Point" U.
And this way, all of them have to go exactly the same distance Delta longer as if they had choosen their direct way!
Where is this "Roundabout-Point" U, and how long is the common additional distance Delta ???

P.S.: Delta=D(a,b,c) is naturally symmetric in the variables a,b,c. So beautiful... !!

for advanced mathematicians: U lies in height h over the triangle-plane (hiker's-lodge on top of roundabout-hill!)
Delta=D(a,b,c,h)...
Solution_3


©1998 by

PiF



No.4 : Wired Functions


Solution: much 'too easy' to be mentioned here ... ;-)



©2000 by

PiF




No.5 : (Not Really) The Longest
Chess-Puzzle of the World ;-))


..the pieces move according to the rules of chess.
lokes somewhat easy, but actually each piece has only the minimal number of moves to get to its target.
So how to solve the muddle in the middle???


©2002 by

PiF



No.6 : Tricky Three D



Diameter of the rods : d = 1 ;

Length of the rods :     L = ??? (Distance between the outermost points of contact)
and here for real!...



©2003 by

F.Pi