MathDB

BMT 2022 Algebra Tiebreaker p2

Source:

9/27/2023

Suppose that

(i - 1)^{11}

is a root of the quadratic

x^2 + Ax + B

for integers

A

and

B

, where

i =\sqrt{-1}

. Compute the value of

A + B

.

algebra

BMT 2022 Discrete Tiebreaker p2

Source:

9/27/2023

A positive integer is called extra-even if all of its digits are even. Compute the number of positive integers

n

less than or equal to

2022

such that both

n

and

2n

are both extra-even.

combinatoricsnumber theory

BMT 2022 Geometry Tiebreaker #2

Source:

8/12/2023

Let

ABCD

be a unit square. Points

E

and

F

are chosen on line segments

\overline{BC}

and

\overline{CD}

, respectively, such that the area of

ABEF D

is three times the area of triangle

\vartriangle ECF

. Compute the maximum possible area of triangle

\vartriangle AEF

.

geometry

BMT 2022 General Tiebreaker #2

Source:

3/9/2024

Call a positive whole number rickety if it is three times the product of its digits. There are two

2

-digit numbers that are rickety. What is their sum?

number theory

Tie 2