MathDB

Speed P4

Source:

10/16/2021

Let

a

,

b

, and

c

be real numbers such that

0\le a,b,c\le 5

and

2a + b + c = 10

. Over all possible values of

a

,

b

, and

c

, determine the maximum possible value of

a + 2b + 3c

.
Proposed by Andrew Wen

MOAA 2021speedalgebrainequalities

Accuracy P4

Source:

10/16/2021

Compute the number of two-digit numbers

\overline{ab}

with nonzero digits

a

and

b

such that

a

and

b

are both factors of

\overline{ab}

.
Proposed by Nathan Xiong

MOAA 2021Accuracy

Team Round P4

Source:

10/16/2021

Compute the number of ordered triples

(x,y,z)

of integers satisfying

x^2+y^2+z^2=9.

Proposed by Nathan Xiong

MOAA 2021team

Gunga P4

Source:

10/16/2021

How many of the following capital English letters look the same when rotated

180^\circ

about their center?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Proposed by William Yue

MOAA 2021Gunga

4