Question 86889
1.  world population is approx 6.6 billion ... 3 ft by 3 ft is a square yard, so 6.6 billion square yards


1760yd=1mi ... 6,600,000,000/1760/1760=approx 2131sq mi ... this is a square approx 46.2 mi on a side



2.  If you picture a circular cross-section of the ball with a diameter going to the center of the bottom of the hole, a triangle formed by the edge of the hole and the ends of the diameter is a right triangle (inscribed in a semicircle).
  Using the diameter (which is the hypotenuse) as the base of the triangle, the altitude is the radius of the hole (20 inches).
  This altitude divides the hypotenuse such that the altitude is the geometric mean of the segments ... or 8:40::40:x ... so x=200 ... making the diameter 8+200 or 208 and the radius 104



3. Take 1 nail from the first barrel, 2 from the next, 4 from the next, etc.; lastly taking 2^9 (512) nails from the 10th barrel

Weigh the nails and subtract 1023 (2^10-1) from the total

Multiply this number by 10 to avoid problems with the decimal point

Convert the resulting amount into binary (1's and 0's) and the barrels will be ordered starting with the rightmost (least significant) digit

The barrels with the heavier nails will be 1's and the lighter nails will be 0's