Tag Archives: Test your intuition

Test Your Intuition (7)

Consider the following game: you have a box that contains one white ball and one black ball. You choose a ball at random and then return it to the box. If you chose a white ball then a white ball is added to … Continue reading

Posted in Probability, Test your intuition | Tagged | 26 Comments

Test Your Intuition (6)

This is not as clear cut a question as the earlier ones, and if you do not know an answer then it will be difficult to figure one out just based on intuition. (But perhaps possible). If you are intrigued by … Continue reading

Posted in Test your intuition | Tagged | 12 Comments

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