MathDB

Tie 3

Part of 2015 BMT Spring

Problems(2)

BMT 2015 Geometry Tiebreaker #3

Source:

8/12/2023
The permutohedron of order 33 is the hexagon determined by points (1,2,3)(1, 2, 3), (1,3,2)(1, 3, 2), (2,1,3)(2, 1, 3), (2,3,1)(2, 3, 1), (3,1,2)(3, 1, 2), and (3,2,1)(3, 2, 1). The pyramid determined by these six points and the origin has a unique inscribed sphere of maximal volume. Determine its radius.
geometry3D geometryanal
BMT 2015 Spring - Individual Tiebreaker #3

Source:

8/12/2023
A bag contains 1212 marbles: 33 red, 44 green, and 55 blue. Repeatedly draw marbles with replacement until you draw two marbles of the same color in a row. What is the expected number of times that you will draw a marble?
combinatorics