MathDB

Speed P3

Source:

10/16/2021

Find the number of ordered pairs

(x,y)

, where

x

and

y

are both integers between

1

and

9

, inclusive, such that the product

x\times y

ends in the digit

5

.
Proposed by Andrew Wen

MOAA 2021speed

Accuracy P3

Source:

10/16/2021

Arnav is placing three rectangles into a

3 \times 3

grid of unit squares. He has a

1\times 3

rectangle, a

1\times 2

rectangle, and a

1\times 1

rectangle. He must place the rectangles onto the grid such that the edges of the rectangles align with the gridlines of the grid. If he is allowed to rotate the rectangles, how many ways can he place the three rectangles into the grid, without overlap?
Proposed by William Yue

MOAA 2021Accuracy

Team Round P3

Source:

10/16/2021

For two real numbers

x

and

y

, let

x\circ y=\frac{xy}{x+y}

. The value of

1 \circ (2 \circ (3 \circ (4 \circ 5)))

can be expressed as

\frac{m}{n}

for relatively prime positive integers

m

and

n

. Compute

m+n

.
Proposed by Nathan Xiong

MOAA 2021team

Gunga P3

Source:

10/16/2021

What is the last digit of

2021^{2021}

?
Proposed by Yifan Kang

MOAA 2021Gunga

3

Problems(4)