MathDB

1

Part of ICMC 6

Problems(2)

Two lines divide square

Source: ICMC 2023 Round 1 P1

11/28/2022
Two straight lines divide a square of side length 11 into four regions. Show that at least one of the regions has a perimeter greater than or equal to 22.
Proposed by Dylan Toh
college contestscombinatorial geometryICMC
RIP Atlantis

Source: ICMC 2023 Round 2 P1

3/1/2023
The city of Atlantis is built on an island represented by [−1,1][ -1, 1], with skyline initially given by f(x)=1−∣x∣f(x) = 1 - |x| . The sea level is currently y=0y=0, but due to global warming, it is rising at a rate of 0.010.01 a year. For any position −1<x<1-1 < x < 1, while the building at xx is not completely submerged, then it is instantaneously being built upward at a rate of rr per year, where rr is the distance (along the xx-axis) from this building to the nearest completely submerged building. How long will it be until Atlantis becomes completely submerged?
Proposed by Ethan Tan
ICMCalgebracollege contestsabsolute value