MathDB

2

Part of 2023 MOAA

Problems(4)

2023 MOAA Speed P2

Source:

10/13/2023
In the coordinate plane, the line passing through points (2023,0)(2023,0) and (−2021,2024)(-2021,2024) also passes through (1,c)(1,c) for a constant cc. Find cc.
Proposed by Andy Xu
MOAA 2023
MOAA Accuracy P2

Source:

10/13/2023
Let ABCDABCD be a square. Let MM be the midpoint of BCBC and NN be the point on ABAB such that 2AN=BN2AN=BN. If the area of △DMN\triangle DMN is 15, find the area of square ABCDABCD.
Proposed by Harry Kim
MOAA 2023
2023 MOAA Team P2

Source:

10/14/2023
Let ABCDABCD be a square with side length 66. Let EE be a point on the perimeter of ABCDABCD such that the area of △AEB\triangle{AEB} is 16\frac{1}{6} the area of ABCDABCD. Find the maximum possible value of CE2CE^2.
Proposed by Anthony Yang
MOAA 2023
2023 MOAA Gunga P2

Source:

10/15/2023
Harry wants to put 55 identical blue books, 33 identical red books, and 11 white book on his bookshelf. If no two adjacent books may be the same color, how many distinct arrangements can Harry make?
Proposed by Anthony Yang
MOAA 2023