Two relatively easy math problems to challenge the gray matter of energetic Brane Space readers:
1) Find the smallest integer that:
- When divided by 3 has a remainder of 1.
- When divided by 4 has a remainder of 2.
- When divided by 5 has a reminder of 3.
- When divided by 6 has a remainder of 4
- When divided by 7 has a remainder of 5
2) You run an enterprise that makes cone-shaped paper cups. You start with a round piece of paper (radius = 1). Then remove one sector, after which you connect the two straight edges to form a cone.
Find the maximum ratio of volume to surface area.
(Hint: You will need to use some basic differential calculus)
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