Category Archives: Test your intuition

Test Your Intuition (5)

  (Not such a set) consider a planar set A with the following property. In every direction, the distance between the two parallel lines that touch A from both sides is the same! Must A be a circle?

Posted in Convexity, Test your intuition | Tagged | 4 Comments

Answer To Test Your Intuition (4)

Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading

Posted in Probability, Test your intuition | Tagged , | 1 Comment

Answer to Test Your Intuition (3)

Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading

Posted in Geometry, Test your intuition | Tagged | 2 Comments

Test Your Intuition (3)

Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in .

Posted in Geometry, Test your intuition | Tagged | 10 Comments

Test Your Intuition (2)

Question: Let be the cube in centered at the origin and having -dimensional volume equal to one.  What is the maximum -dimensional volume of when  is a hyperplane? Can you guess the behavior of when ? Can you guess the plane which … Continue reading

Posted in Convexity, Test your intuition | Tagged | 5 Comments

Test Your Intuition (1)

Question:  Suppose that we sequentially place balls into boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability balls in it. Suppose instead that … Continue reading

Posted in Computer Science and Optimization, Probability, Test your intuition | Tagged | 11 Comments