MathDB

2

Part of 2021 MOAA

Problems(4)

Speed P2

Source:

10/16/2021
[asy] size(5cm); defaultpen(fontsize(6pt)); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle); draw((0,0)--(-4,0)--(-4,-4)--(0,-4)--cycle); draw((1,-1)--(1,3)--(-3,3)--(-3,-1)--cycle); draw((-1,1)--(-1,-3)--(3,-3)--(3,1)--cycle); draw((-4,-4)--(0,-4)--(0,-3)--(3,-3)--(3,0)--(4,0)--(4,4)--(0,4)--(0,3)--(-3,3)--(-3,0)--(-4,0)--cycle, red+1.2); label("1", (-3.5,0), S); label("2", (-2,0), S); label("1", (-0.5,0), S); label("1", (3.5,0), S); label("2", (2,0), S); label("1", (0.5,0), S); label("1", (0,3.5), E); label("2", (0,2), E); label("1", (0,0.5), E); label("1", (0,-3.5), E); label("2", (0,-2), E); label("1", (0,-0.5), E); [/asy]
Compute the area of the resulting shape, drawn in red above.
Proposed by Nathan Xiong
MOAA 2021speed
Accuracy P2

Source:

10/16/2021
On Andover's campus, Graves Hall is 6060 meters west of George Washington Hall, and George Washington Hall is 8080 meters north of Paresky Commons. Jessica wants to walk from Graves Hall to Paresky Commons. If she first walks straight from Graves Hall to George Washington Hall and then walks straight from George Washington Hall to Paresky Commons, it takes her 88 minutes and 4545 seconds while walking at a constant speed. If she walks with the same speed directly from Graves Hall to Paresky Commons, how much time does she save, in seconds?
Proposed by Nathan Xiong
MOAA 2021Accuracy
Team Round P2

Source:

10/16/2021
Four students Alice, Bob, Charlie, and Diana want to arrange themselves in a line such that Alice is at either end of the line, i.e., she is not in between two students. In how many ways can the students do this?
Proposed by Nathan Xiong
MOAA 2021team
Gunga P2

Source:

10/16/2021
Add one pair of brackets to the expression 1+2×3+4×5+61+2\times 3+4\times 5+6 so that the resulting expression has a valid mathematical value, e.g., 1+2×(3+4×5)+6=531+2\times (3 + 4\times 5)+6=53. What is the largest possible value that one can make?
Proposed by Nathan Xiong
MOAA 2021Gunga