MathDB

3

Part of 2019 BMT Spring

Problems(5)

Squares that sum to 50 (BMT 2019 Algebra #3)

Source:

5/4/2019
There are several pairs of integers (a,b) (a, b) satisfying a2−4a+b2−8b=30 a^2 - 4a + b^2 - 8b = 30 . Find the sum of the sum of the coordinates of all such points.
Think inside the quadrilateral parallelogram! (BMT 2019 Geo #3)

Source:

5/10/2019
Let ABCD ABCD be a parallelogram with BC=17 BC = 17 . Let M M be the midpoint of BC‾ \overline{BC} and let N N be the point such that DANM DANM is a parallelogram. What is the length of segment NC‾ \overline{NC} ?
geometryparallelogram
This is a graph theory problem?! (BMT 2019 Discrete #3)

Source:

5/23/2019
There are 15 people at a party; each person has 10 friends. To greet each other each person hugs all their friends. How many hugs are exchanged at this party?
graph theory
cylinder rolling with water inside 2019 BMT Team 3

Source:

1/5/2022
A cylinder with radius 55 and height 11 is rolling on the (unslanted) floor. Inside the cylinder, there is water that has constant height 152\frac{15}{2} as the cylinder rolls on the floor. What is the volume of the water?
geometry3D geometrycylinder
2019 BMT Individual 3

Source:

1/9/2022
If f(x+y)=f(xy)f(x + y) = f(xy) for all real numbers xx and yy, and f(2019)=17f(2019) = 17, what is the value of f(17)f(17)?
algebra