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as for the 5 dots question. i go for the houseshape :)

uh correction, i do not go for the houseshape...

mr. spock: how many dots can you place in 4d space without intersecting grid planes (intersection of grid spaces in 3d)? :)

anes: 16

But you should have solved that! :)

no i don't mean the lines don't intersect grid points. they shouldn't intersect the lines and the planes :)

planes? I am not sure how you define them?

solve the 3d counterpart first then. you're going to place dots on a 3d grid with lines. but lines drawn from dot pairs won't intersect the grid lines also. how far can you go?

well, that is essentially the same as the 2d problem, so its 4. Or I still misunderstand the problem :)

Hey Spock, great extrapolation of the problem :) Now, what about 1d space and 3 points? :P

Trick question: Why is this dog overweight?

spock: it's 4 for 3d but it's not 4 for 4d (obviously less than 4).

Oh fuck... I needed a lot of years to recover from my math-freakness and don't talk about this kind of puzzles. Now I'm starting to do it again... I would not be a problem if talking about maths and having sex were compatible.

anes: If the planes in 4d are 2d its still 4 points, if you assume they are 3d its down to 2.

solved in a dog-space.

the planes are 2d and the answer still is not 4 :)

anes, still not sure I get your definition right. You can simply reduce the 4d problem to 2d by setting two of the coordiantes elements to 0. Due to that the number of solutions can not be smaller than in 2d.

in 3d, if you set the extra coordinate to 0 (if you put all dots on z=0) then they surely intersect at a grid line.



and a correction to the question. dot pairs must be 2 units away from each other. otherwise you can put 8 dots in 3d at the vertices of a cube with 1 edge length.

the answer is 4 for 3d but the result doesn't come directly from texel's question.

(0,0,0) - (1,2,0) intersects
(0,0,0) - (1,2,1) doesn't.
i hope you get the idea now.

Since I was accepted into Mensa by solving the chess puzzle, I am now qualified to post puzzles. And here's a variation on a classic puzzle that's considered nigh-impossible to solve for quantum physicists but medium-rare for evolutionary biologists:

What did the little mountain say to the big mountain?

Logic class.. bit longer than a year ago... and the best thing.. I FORGOT EVERYTHING MUHUAHAUHUAH :D

In first-angle projection we have this two views of an object:



(frontal and left views)

Can you draw the plan or tell what shape the object has?

Note: there are not occluded lines. (else would be drawn dotted)

Eh.. cylinder NOT box? Better puzzles please.

texel: the square with dot in middle actually solves the problem because your rules say that intersection points which match the original points are valid.

a better puzzle: does the set of all sets that don't include themselves include itself?

it's difficult for rocket engineers but it's mediocre level for ocean zoologists.