MathDB

TB1. Two not necessarily distinct positive integers

a,b

are randomly chosen from the set

\{1,2,\ldots, 20\}

. Find the expected value of the number of distinct prime factors of

ab

.
Proposed by Harry Kim
TB2. Square

ABCD

has side length

15

. Let

E

and

F

be points on

AD

and

BC

respectively such that

AE = 5

and

BF = 5

. Find the area of intersection between triangles

\triangle{AFC}

and

\triangle{BED}

.
Proposed by Andy Xu
TB3. If

x

and

y

satisfy

\frac{1}{x}+\frac{1}{y} = 2

\frac{x}{y}+\frac{y}{x} = 3

find

xy

.
Proposed by Harry Kim and Andy Xu

Problem Statement