# Are you a genius?

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.
+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?
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