MathDB

2023 MOAA Speed P7

Source:

10/13/2023

Andy flips a strange coin for which the probability of flipping heads is

\frac{1}{2^k+1}

, where

k

is the number of heads that appeared previously. If Andy flips the coin repeatedly until he gets heads 10 times, what is the expected number of total flips he performs?
Proposed by Harry Kim

MOAA 2023

2023 MOAA Accuracy P7

Source:

10/13/2023

Pentagon

ANDD'Y

has

AN \parallel DY

and

AY \parallel D'N

with

AN = D'Y

and

AY = DN

. If the area of

ANDY

is 20, the area of

AND'Y

is 24, and the area of

ADD'

is 26, the area of

ANDD'Y

can be expressed in the form

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Find

m+n

.
Proposed by Andy Xu

MOAA 2023

2023 MOAA Team P7

Source:

10/14/2023

In a cube, let

M

be the midpoint of one of the segments. Choose two vertices of the cube,

A

and

B

. What is the number of distinct possible triangles

\triangle AMB

up to congruency?
Proposed by Harry Kim

MOAA 2023

2023 MOAA Gunga P7

Source:

10/15/2023

Written in mm/dd format, a date is called cute if the month is divisible by the day. For example, the date cute is a cute date because

8

is divisible by

2

. Find the number of cute dates in a year.
Proposed by Andy Xu

MOAA 2023

7

Problems(4)