MathDB

2.6 1.2

Part of 2021 CMIMC

Problems(2)

2021 Geo Div 1 P2 (Div 2 P6)

Source:

3/2/2021
In convex quadrilateral ABCDABCD, ∠ADC=90∘+∠BAC\angle ADC = 90^\circ + \angle BAC. Given that AB=BC=17AB = BC = 17, and CD=16CD = 16, what is the maximum possible area of the quadrilateral?
Proposed by Thomas Lam
geometry
2021 Combo Div 1 P2 (Div 2 P6)

Source:

3/2/2021
Adam is playing Minesweeper on a 9×99\times9 grid of squares, where exactly 13\frac13 (or 27) of the squares are mines (generated uniformly at random over all such boards). Every time he clicks on a square, it is either a mine, in which case he loses, or it shows a number saying how many of the (up to eight) adjacent squares are mines.
First, he clicks the square directly above the center square, which shows the number 44. Next, he clicks the square directly below the center square, which shows the number 11. What is the probability that the center square is a mine?
Proposed by Adam Bertelli
combinatorics