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.
i think i will leave them here for more days.
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