MathDB

1

Part of 2019 BMT Spring

Problems(5)

diophantine x^2 - 9x + 18 < 0

Source: BMT 2019 Spring Algebra 1

10/8/2021
How many integers x x satisfy x2−9x+18<0 x^2 - 9x + 18 < 0 ?
number theorytrinomialalgebra
Who's AEKS-ited for some geo?! (BMT 2019 Geo #1)

Source:

5/9/2019
Consider the figure (attached), where every small triangle is equilateral with side length 1. Compute the area of the polygon AEKS AEKS .
(Fun fact: this problem was originally going to ask for the area of DANK DANK , as in "dank memes!")
fair coin is repeatedly flipped until 2019 consecutive coin flips are same

Source: BMT 2019 Spring Discrete 1

10/8/2021
A fair coin is repeatedly flipped until 20192019 consecutive coin flips are the same. Compute the probability that the first and last flips of the coin come up differently.
combinatoricsprobability
2019 BMT Team 1

Source:

1/7/2022
Find the maximum integral value of kk such that 0≤k≤20190 \le k \le 2019 and ∣e2πik2019−1∣|e^{2\pi i \frac{k}{2019}} - 1| is maximal.
algebra
2019 BMT Individual 1

Source:

1/9/2022
Let pp be a polynomial with degree less than 44 such that p(x)p(x) attains a maximum at x=1x = 1. If p(1)=p(2)=5p(1) = p(2) = 5, find p(10)p(10).
algebra