MathDB

BMT 2015 Spring - Geometry 2

Source:

12/30/2021

ABCDEF

is a regular hexagon. Let

R

be the overlap between

\vartriangle ACE

and

\vartriangle BDF

. What is the area of

R

divided by the area of

ABCDEF

?

geometry

2015 BMT Team 2

Source:

1/6/2022

Compute the sum of the digits of

1001^{10}

number theory

2015 BMT Spring Analysis 2

Source:

1/20/2022

Let

g(x)=1+2x+3x^2+4x^3+\ldots

. Find the coefficient of

x^{2015}

of

f(x)=\frac{g(x)}{1-x}

.

algebraPolynomials

2015 BMT Spring Discrete 2

Source:

1/20/2022

Determine the largest integer

n

such that

2^n

divides the decimal representation given by some permutation of the digits

2

,

0

,

1

, and

5

. (For example,

2^1

divides

2150

. It may start with

0

.)

number theory

BMT 2015 Spring - Individual 2

Source:

1/22/2022

Suppose we list the decimal representations of the positive even numbers from left to right. Determine the

2015^{th}

digit in the list.

algebra

2