MathDB

2

Part of 2021 BMT

Problems(4)

BMT Discrete #2 - Counting Up and Down

Source:

11/29/2021
Alice is counting up by fives, starting with the number 33. Meanwhile, Bob is counting down by fours, starting with the number 20212021. How many numbers between 33 and 20212021, inclusive, are counted by both Alice and Bob?
number theoryBmt
BMT 2021 Guts Round p2

Source:

10/7/2022
The battery life on a computer decreases at a rate proportional to the display brightness. Austin starts off his day with both his battery life and brightness at 100%100\%. Whenever his battery life (expressed as a percentage) reaches a multiple of 2525, he also decreases the brightness of his display to that multiple of 2525. If left at 100%100\% brightness, the computer runs out of battery in 11 hour. Compute the amount of time, in minutes, it takes for Austin’s computer to reach 0%0\% battery using his modified scheme.
algebra
BMT 2021 Geometry #2

Source:

8/12/2023
Compute the area of the smallest triangle which can contain six congruent, non-overlapping unit circles.
geometry
2021 BMT Algebra #2

Source:

3/10/2024
Let ff and gg be linear functions such that f(g(2021))−g(f(2021))=20f(g(2021))-g(f(2021)) = 20. Compute f(g(2022))−g(f(2022))f(g(2022))- g(f(2022)). (Note: A function h is linear if h(x)=ax+bh(x) = ax + b for all real numbers xx.)
algebra