MathDB

p13 Let

ABCD

be a square. Points

E

and

F

lie outside of

ABCD

such that

ABE

and

CBF

are equilateral triangles. If

G

is the centroid of triangle

DEF

, then find

\angle AGC

, in degrees.
p14 The silent reading

s(n)

of a positive integer

n

is the number obtained by dropping the zeros not at the end of the number. For example,

s(1070030) = 1730

. Find the largest

n < 10000

such that

s(n)

divides

n

and

n\ne s(n)

.
p15 Let

ABCDEFGH

be a regular octagon with side length

12

. There exists a region

R

inside the octagon such that for each point

X

R

, exactly three of the rays

AX

BX

CX

DX

GX

, and

HX

intersect segment

EF

. If the area of region

R

can be expressed as

a -b\sqrt{c}

for positive integers

a, b, c

with

c

squarefree, find

a + b + c

Problem Statement