MathDB

4

Part of 2022 BMT

Problems(5)

BMT 2022 Fall Algebra P4

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5/5/2023
Find all real xx such that ⌊x⌈x⌉⌋=2022.\lfloor x \lceil x \rceil \rfloor = 2022. Express your answer in interval notation.
floor functionceiling function
BMT 2022 Fall Discrete P4

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5/6/2023
Richard and Shreyas are arm wrestling against each other. They will play 1010 rounds, and in each round, there is exactly one winner. If the same person wins in consecutive rounds, these rounds are considered part of the same “streak”. How many possible outcomes are there in which there are strictly more than 33 streaks? For example, if we denote Richard winning by RR and Shreyas winning by S,S, SSRSSRRRRRSSRSSRRRRR is one such outcome, with 44 streaks.
BMT 2022 Geometry #4 / General #21

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8/12/2023
On regular hexagon GOBEARGOBEAR with side length 22, bears are initially placed at G,B,AG, B, A, forming an equilateral triangle. At time t=0t = 0, all of them move clockwise along the sides of the hexagon at the same pace, stopping once they have each traveled 11 unit. What is the total area swept out by the triangle formed by the three bears during their journey?
geometry
BMT 2022 Guts #4

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8/31/2023
Compute the number of primes less than 4040 that are the sum of two primes.
number theory
BMT 2022 Fall General P4 (im not very good at asy)

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5/7/2023
Big Chungus has been thinking of a new symbol for BMT, and the drawing below is what he came up with. If each of the 1616 small squares in the grid are unit squares, what is the area of the shaded region?
Idk asyBmtgeneral