MathDB

2

Part of 2019 ASDAN Math Tournament

Problems(3)

2019 Discrete Tiebreaker #2

Source:

10/5/2022
Let P1,P2,…,P720P_1,P_2,\dots,P_{720} denote the integers whose digits are a permutation of 123456123456, arranged in ascending order (so P1=123456P_1=123456, P2=123465P_2=123465, and P720=654321P_{720}=654321). What is P144P_{144}?
2019Discrete Math Tiebreaker
2019 Geometry #2

Source:

9/10/2023
A square and a line intersect at a 45o45^o angle. The line bisects the square into two unequal pieces such that the area of one piece is twice that of the other. If the square has side length 66, compute the length of the cut due to the line. https://cdn.artofproblemsolving.com/attachments/6/4/2eb33fb9766497d25d342001cdbae9a7ffd4b4.png
geometry2019
2019 Geometry Tiebreaker # 2

Source:

9/10/2023
Consider a triangle △ABC\vartriangle ABC with AB=5AB = 5 and BC=4BC = 4. Let GG be the centroid of the triangle, and let PP lie on line AGAG such that AG=GPAG = GP and P≠AP\ne A. Suppose that PP lies on the circumcircle of △ABC\vartriangle ABC. Compute CACA.
Geometry Tiebreaker2019