20050715, 07:35  #23 
Jun 2003
The Texas Hill Country
2101_{8} Posts 
So, Mally,
Your reasoning is faulty... If you consider the orientation of the tetrahedron to be critical, and differentiating with respect to distinct cases, why do you stop with up vs down? Is an upright tetrahedron with one side of the base oriented in a NorthSouth direction that same as one where that side is oriented in an EastWest direction? What about my example of a ravine? There the tetrahedron is oriented neither up nor down. Since you claim that there are exactly two distinct solutions, which one is mine? 
20050715, 16:36  #24 
Aug 2003
Snicker, AL
1111000000_{2} Posts 
I have to agree with Wacky and Xilman on this one. A tetrahedron is the only viable form that fits the requirements, but the tetrahedron can be oriented vertex up, vertex down, or vertex at an angle as per the example of the ravine with two trees in the bottom and two trees up top. By extension, the "ravine" could be the dip between two mountains of varying heights such that the tetrahedron could assume just about any angle.
I vote one solution, the tetrahedron. Orient it any way you choose. 
20050717, 07:32  #25 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Lateral thinking puzzle.
[QUOTE=Wacky]So, Mally,
Your reasoning is faulty...]UnQuote/ :surprised Lateral thinking puzzle. After reviewing the post above I am retracting my statement that there are only two solutions. Lets see how the idea developed. Paul hit the nail on the head by giving the general solution which can be represented by a tetrahedron. [tetra(h)] Numbers explained that its a hypothetical frame and not a mechanical one. Wacky went a step further when he noted a depression would also serve the purpose implying an inverted tetra (h). Subsequently he pointed out that on a flat surface itself there are infinite positions. Fusion Power on wackys tip introduced the ravine where the tetra (h) could be accommodated according to virtually any configuration and went off to sleep !.. It s not the case of who is right or wrong or allying oneself to any party. This could lead to a flaming war. Just the day before Prof. ewmayer locked out a post for this very same reason. Please read his reasons and guidelines in ‘Exponential digits’ Each post contributes to the preceding one. I would dare say even wrong posts help in the final analysis. Napoleon Hill says “When two or more minds get together the third mind is formed”. Very true!. Since I introduced the problem I learnt very much more than when I posted it It will be interesting to know how Edward de Bono himself tackled this problem. I quote from his book ‘Lateral thinking’. Quote [ .. but one tree is planted at the top of a hill and the other trees are planted on the side of the hill. This makes them all equidistant from one another (in fact they are at the angles of a tetra(h). One can also solve the problem by placing one tree at the bottom of a hole and the others around the edges of the hole] Unquote/ Hope this clears the air and my statement is acceptable. Mally . 
20050805, 07:14  #26  
Jun 2003
1605_{10} Posts 
Quote:
Actually there are infinite answers to this question. The 4 corners of any rohmbus will work and there are infinite of them. Citrix 

20050805, 08:30  #27  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2^{3}×3×5×97 Posts 
Quote:
A rhombus is defined as a plane quadrilateral with each pair of opposite sides parallel. One special case of a rhombus is a square. Opposite corners of a square are separated by a distance sqrt(2) times adjacent corners, so the four corners are not all the same distance from each other. In Euclidean space, the four points must be at the vertices of a regular tetrahedron. There are an infinite number of orientations of a tetrahedron, so an infinite number of solutions. Paul 

20051124, 15:27  #28 
"GIMFS"
Sep 2002
Oeiras, Portugal
622_{16} Posts 
That leads us to the original topic of this thread: the hapless chap that killed himself.
He was actually quite desperate about solving the gardener´s puzzle... Thought about several types of frames (mechanical and nonmechanical ) and eventually fell asleep on a rhombusshaped bed. Woke up with the loud noise and ran to the front door to find a huge (regular) tetrahedron in the middle of the road. And he sighed: "Silly me! This is the one and only solution to the problem" . And he ran up the stairs in shame, went to a different room to avoid being misled once again by the shape of his bed and shot himself using a conic bullet. His last thought was: "Perhaps a coneshaped frame, with the appropriate height, will also be a solution... Oh well, forget about it, this problem is killing me!" 
20051124, 17:16  #29 
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Lateral thinking puzzle.
Lycorn that's a fitting ending to an unusual story. If you include the background to it, it may become a best seller and earn you millions of euros if you only publish it.
Thank you I enjoyed the humour you have inculcated to a boring problem which has so many erroneous solutions! It was as is said in Latin 'Pons arsinnorum' and this translated literally is the 'Bridge of Asses' as my geometry teacher would say of the 6th Theorem of Euclid if I remember it well. Mally 
20051125, 22:06  #30 
"GIMFS"
Sep 2002
Oeiras, Portugal
2×5×157 Posts 

20051126, 10:33  #31  
May 2003
3×5×17 Posts 
Quote:
Put 2 trees at opposite sides of the top of the grand canyon, and two at the base of the valley itself. However, you're solution of just placing them in 4 different continents is the best one, as it's not very easy. Do you know where works? (I can google for the/a solution, as ISTR the newsgroup and the poster that solved it.) And now solve in Lobachevskian space! Great thread hijack, BTW, to whomever performed it! 

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