MathDB

BMT 2017 Spring - Geometry 4

Source:

12/30/2021

How many lattice points

(v, w, x, y, z)

does a

5

-sphere centered on the origin, with radius

3

, contain on its surface or in its interior?

geometry

acute <AOB by 2 darts on a circular board 2017 BMT Team 4

Source:

1/5/2022

2

darts are thrown randomly at a circular board with center

O

, such that each dart has an equal probability of hitting any point on the board. The points at which they land are marked

A

and

B

. What is the probability that

\angle AOB

is acute?

geometryangleacute

2017 BMT Individual 4

Source:

1/9/2022

There are two

3

-digit numbers which end in

99

. These two numbers are also the product of two integers which differ by

2

. What is the sum of these two numbers?

number theory

2017 BMT Discrete #4

Source:

3/9/2024

What is the greatest multiple of

9

that can be formed by using each of the digits in the set

\{1, 3,5, 7, 9\}

at most once.

number theory

2017 BMT Analysis #4

Source:

3/10/2024

Find the value of

\frac12+\frac{4}{2^2} +\frac{9}{2^3} +\frac{16}{2^4} + ...

algebra

4