Are you a genius?

Anonymous
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?

Are you a genius?


2) Find the necessary and sufficient number of non-attacking queens to cover a cubic chess-board of 64 boxes

Are you a genius?


3) What is the minimum number of squares that would be sufficient to create the following pattern?

Are you a genius?


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.

Are you a genius?


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.
+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.

i think i will leave them here for more days.
Are you a genius?
3
7
Add Opinion