MathDB

16

Part of 2015 BMT Spring

Problems(2)

AB=BC=CD=DE=EA=1, <ABC=<BCD=<CDE=<DEA=90^o 2015 BMT Team 16

Source:

1/4/2022
Five points A,B,C,DA, B, C, D, and EE in three-dimensional Euclidean space have the property that AB=BC=CD=DE=EA=1AB = BC = CD = DE = EA = 1 and ∠ABC=∠BCD=∠CDE=∠DEA=90o\angle ABC = \angle BCD =\angle CDE = \angle DEA = 90^o . Find all possible cos⁡(∠EAB)\cos(\angle EAB).
geometry3D geometryequal anglesequal segments
BMT 2015 Spring - Individual 16

Source:

1/22/2022
A binary decision tree is a list of nn yes/no questions, together with instructions for the order in which they should be asked (without repetition). For instance, if n=3n = 3, there are 1212 possible binary decision trees, one of which asks question 22 first, then question 33 (followed by question 1 1) if the answer was yes or question 11 (followed by question 33) if the answer was no. Determine the greatest possible kk such that 2k2^k divides the number of binary decision trees on n=13n = 13 questions.
combinatorics