Tag Archives: Test your intuition

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