Brain Teasers

[anileve]

Well if you think of it in terms of dimensions, then technically the lines are parallel in fact precisely supporting the laws of Euclidean space. The problem never inidicated it as a one dimensional figure.

[Sip]

Solution to Problem #2

There are 5 regions in the figure. Two regions have 4 eges and three regions have 5 edges each. Let's call them even and odd regions. When we are drawing the line, a an even region is good since we can start from the outside, cross all edges, and still be on the outside. But with an odd region, if we start from outside we will be "stuck" inside of it and if we start from inside we will end up outside once we cross all edges.

So now, we have 3 odd regions. If the line starts from outside of all of them, it is going to get stuck in one of the regions once all the edges of that region are crossed and well be stuck.

If the line starts from the inside of one of the odd figures, the line will end up outside but will be stuck inside one of the other remaining two odd regions. In the end, we will have one odd region left whose edges are not crossed. Thus, this problem has no solution.

[sSsflamesSs]

Originally posted by anileve Well if you think of it in terms of dimensions, then technically the lines are parallel in fact precisely supporting the laws of Euclidean space. The problem never inidicated it as a one dimensional figure.

I think that the 2-D layout is assumed. My dad told me a more "fun" version of this problem, which involved 3 neighbors (Points 1, 2, 3) that are pissed off at each other and need to avoid each other at all costs, when they go to the grocery store, bakery, and bank (Points A, B, C).

[Sip]

Hehehehe ... I didn't want to say it like that since the answer could then easily be looked up on the web ... the problem is also known as "3 houses 3 utilities". In graph theory, that structure is known as the "K3,3" graph (bipartite graph) which can also be shown by Euler's formula to be non-planar ... as in can't be drawn in a 2D plane ... that is by far the easiest way to solve the problem but requires knowledge of graph theory.

[anileve]

Originally posted by Seapahn Ok here is the solution to problem #1.

This is not a rigorous proof but should be good enough

Well it's not... You should have worded the problem better, according to the nature of the problem and the wording my solution doesn't brake any rules and I consider it a valid solution. So there!

[sSsflamesSs]

Have you guys attempted my "3 KIDS" problem? It's not too difficult, but it's fun when you figure it out.

[Sip]

Originally posted by anileve Well it's not... You should have worded the problem better, according to the nature of the problem and the wording my solution doesn't brake any rules and I consider it a valid solution. So there!

The problem says draw it such that no two lines intersect. Here is the definition of "intersect" from mathworld. In what you drew, you have parallel lines that "concur" at many points and thus they intersect.

In the solution, lines CAN NOT touch at all.

[anileve]

Originally posted by sSsflamesSs Have you guys attempted my "3 KIDS" problem? It's not too difficult, but it's fun when you figure it out.

Just off the top of my head, which seems to be too obvious to be the answer. The problem is so vague flames...lakot. Highlight.

The ages are 4, 3, 3 The number on the bus is 10

[sSsflamesSs]

Originally posted by anileve Just off the top of my head, which seems to be too obvious to be the answer. The problem is so vague flames...lakot. Highlight.

The ages are 4, 3, 3 The number on the bus is 10

If the answer seems too obvious, then it's most likely incorrect.

Try again.




(If the info I provided seems too vague, then that means you haven't given the problem much thought. The problem provides all the info for one solution. I will provide hints upon request.)

[ckBejug]

Ok Flames, I think I got your 5 houses one, it was fun, like the analytical section of the GRE, but longer... (german has fish green house #4 cofee drinking pince smoker?? See attachment for how i did it)