MathDB

p1. Bahri lives quite close to the clock gadang in the city of Bukit Tinggi West Sumatra. Bahri has an antique clock. On Monday

4

th March

2013

10.00

am, Bahri antique clock is two minutes late in comparison with Clock Tower. A day later, the antique clock was four minutes late compared to the Clock Tower. March

6

2013

the clock is late six minutes compared to Jam Gadang. The following days Bahri observed that his antique clock exhibited the same pattern of delay. On what day and what date in

2014

the antique Bahri clock (hand short and long hands) point to the same number as the Clock Tower?
p2. In one season, the Indonesian Football League is participated by

20

teams football. Each team competes with every other team twice. The result of each match is

3

if you win,

1

if you draw, and

0

if you lose. Every week there are

10

matches involving all teams. The winner of the competition is the team that gets the highest total score. At the end what week is the fastest possible, the winner of the competition on is the season certain?
p3. Look at the following picture. The quadrilateral

ABCD

is a cyclic. Given that

CF

is perpendicular to

AF

CE

is perpendicular to

BD

, and

CG

is perpendicular to

AB

. Is the following statements true? Write down your reasons.

\frac{BD}{CE}=\frac{AB}{CG}+ \frac{AD}{CF}

https://cdn.artofproblemsolving.com/attachments/b/0/dbd97b4c72bc4ebd45ed6fa213610d62f29459.png
p4. Suppose

M=2014^{2014}

. If the sum of all the numbers (digits) that make up the number

M

equals

A

and the sum of all the digits that make up the number

A

equals

B

, then find the sum of all the numbers that make up

B

.
p5. Find all positive integers

n < 200

so that

n^2 + (n + 1)^2

is square of an integer.

Problem Statement