MathDB

2.1

Part of 2022 CMIMC

Problems(3)

2022 Alg/NT Div 2 P1

Source:

2/28/2022
Alice and Bob live on the same road. At time tt, they both decide to walk to each other's houses at constant speed. However, they were busy thinking about math so that they didn't realize passing each other. Alice arrived at Bob's house at 3:19pm3:19\text{pm}, and Bob arrived at Alice's house at 3:29pm3:29\text{pm}. Charlie, who was driving by, noted that Alice and Bob passed each other at 3:11pm3:11\text{pm}. Find the difference in minutes between the time Alice and Bob left their own houses and noon on that day.
Proposed by Kevin You
algebranumber theory
2022 Geo Div 2 P1

Source:

2/28/2022
An equilateral 1212-gon has side length 1010 and interior angle measures that alternate between 90∘90^\circ, 90∘90^\circ, and 270∘270^\circ. Compute the area of this 1212-gon.
Proposed by Connor Gordon
geometry
2022 Combo Div 2 P1

Source:

2/28/2022
A particle starts at (0,0,0)(0,0,0) in three-dimensional space. Each second, it randomly selects one of the eight lattice points a distance of 3\sqrt{3} from its current location and moves to that point. What is the probability that, after two seconds, the particle is a distance of 222\sqrt{2} from its original location?
Proposed by Connor Gordon
combinatorics