MathDB

5

Part of 2017 BMT Spring

Problems(5)

BMT 2017 Spring - Geometry 5

Source:

12/30/2021
Suppose the side lengths of triangle ABCABC are the roots of polynomial x3−27x2+222x−540x^3 - 27x^2 + 222x - 540. What is the product of its inradius and circumradius?
geometry
2017 BMT Team 5

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1/6/2022
You enter an elevator on floor 00 of a building with some other people, and request to go to floor 1010. In order to be efficient, it doesn’t stop at adjacent floors (so, if it’s at floor 00, its next stop cannot be floor 1 1). Given that the elevator will stop at floor 1010, no matter what other floors it stops at, how many combinations of stops are there for the elevator?
combinatorics
2017 BMT Individual 5

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1/9/2022
How many pairs of positive integers (a,b)(a, b) satisfy the equation loga16=blog_a 16 = b?
algebranumber theory
2017 BMT Discrete #5

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3/9/2024
How many subsets of {1,2,...,9}\{1, 2,...,9\} do not contain 22 adjacent numbers?
combinatorics
2017 BMT Analysis #5

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3/10/2024
Find the value of yy such that the following equation has exactly three solutions. ∣∣x−1∣−4∣=y.||x -1|-4|= y.
algebra