Answer these 4 questions in the next 12 hours and you get mho (and a PHD scholarship in MIT!). you need to provide full answers and proof.
1) What is the volume of the smallest possible cube containing 9 unit cubes?
2) Find the necessary and sufficient number of non-attacking queens to cover a cubic chess-board of 64 boxes
3) What is the minimum number of squares that would be sufficient to create the following pattern?
4) Consider the torus, a doughnut-shaped solid that is perfectly circular at each perpendicular cross section, and a Möbius strip, which has a single 180-degree twist and a uniform curvature throughout its length. Suppose a torus is sliced three times by a knife that each time precisely follows the path of such a Möbius strip. What is the maximum number of pieces that can result if the pieces are never moved from their original positions? Note: Each of the Möbius strips is entirely confined to the interior of the torus.
If you answer these successfully please... get the hell out of gag and do something for humanity! lol.
Updates
+1 y
even if you solve 2 in 24 hours you still get mho. and a bit of a help/visualisation with the first for example. if it were with 8 unit cubes, wouldn't it be stacking 4 in a square shape upon four and creating a 2x2x2 unit cube? well if you add a ninth, won't the most economical shape be the 8 cubes arranged as mentioned, touching though the ninth in the middle of its sides, which results in the distancing of the first 8 a little bit? the question is to minimize that distance. i hope i helped.
Updates
+1 y
continuation of the tip for the first problem. in simple words you look for the way to place the ninth cube inbetween the first 8 (the 2x2x2 cube) so that you create the smallest cube possible that can enclose the other 9. you want to minimize the unoccupied volume in that bigger cube.
1. The smallest possible volume of the 9 cubes is possible by melting them and re-casting them in shape of a cube, the volume will be 9 cube units. Side = cube root 9.
2. How does a cubical chess board react? Do queens on each face attack each other? adjacent face, opposite face? I am assuming the queens on each face can only be affected by queens on that face. In that case, every face can have 4 queens each, as a cube has 6 face, then 24 queens. (Ofcourse all the queens except on the top face has to be pasted by glue or else they will fall off, or the chess board should be magnetic)
3. Good lord wasted 4 pages for this one, I am assuming that no line can be erased, but can be overlapped by a cube. I got 17 for this one, but I am not sure if it's the minimum number of cubes I could use.. But the answer has to be 15,16 or 17.
4. This one is hard lol, I think I am gonna fuck this up but bear with me..
The maximum number of pieces will be possible when we assume the knife chips off some part of the torus at every local maxima (ie convex curve) since the knife is following path of a mobius strip. As torus is chopped 3 times, according to me the maximum number of pieces possible are 5.
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+1 y
stopped reading at melting them. where did i mention there are made of metal. they can be wooden. they dont even have to be corporeal. didn't you read my tip for that first problem?
i actually read the rest of your answers too and unfortunately you found nothing. i think i was too confident on gaggers capabilities. it is just that statistically i thought i can find one person that can tackle these problems.
the queens be the way affect the whole cube. or else i'd say 6 chessboards glued together.
wood cannot be melted but I believe plastification can be a viable solution, that can get the job done lol. I didn't read your update until i reached the 4th question, sorry.
Each face has 64 boxes? I thought the figure was the one. It's possible , although can I know the shape? jesus cross or like swastik?
Ow, sorry to disappoint you, what's the answer for the 3rd one though? Was it among the 3 numbers that I stated?
Why do people associate being a genius to exact sciences and numbers? Damn! I'm terrible at that! If I'm only a genious if I know this things, them I'm dumber than a protozoan.
I feel like these could be worded better. Anyways, I don't really care and kinda too lazy to think about, but I'll give it my best minimal effort shot
1- 27 2- I don't know what that even means, but either 6, 8 or 12 3- what is that asking? But anyways, I'd say 1, 11 or 36 depending on what it means 4- I don't know what the fuck it's asking. It doesn't make sense.
Anyways, none of these make you a genius or mit material
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Asker
+1 y
the fact that you didn't even understand what the problems say, says a lot about your ingenuity. but i admit they are problems that tackle very specific kinds of intelligence.
They weren't worded in the most convenient way. If I write "man eating sandwiche", there are connotations. Also, I don't think 4 random questions from a fuckboy to determine how smart I am. I'll take the fact I got accepted into a couple high ranking schools like Vanderbilt and Princeton (went to neither) and have a 155 iq and got accepted into Mensa (I wasn't gonna pay for that shit), including the fact that I maxed out on the memory, logic and puzzle sections
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