MathDB

p1. A rectangular pool has diagonal

17

units and area

120

units

^2

. Joey and Rachel start on opposite sides of the pool when Rachel starts chasing Joey. If Rachel runs

5

units/sec faster than Joey, how long does it take for her to catch him?
p2. Alice plays a game with her standard deck of

52

cards. She gives all of the cards number values where Aces are

1

’s, royal cards are

10

’s and all other cards are assigned their face value. Every turn she flips over the top card from her deck and creates a new pile. If the flipped card has value

v

, she places

12 - v

cards on top of the flipped card. For example: if she flips the

3

of diamonds then she places

9

cards on top. Alice continues creating piles until she can no longer create a new pile. If the number of leftover cards is

4

and there are

5

piles, what is the sum of the flipped over cards?
p3. There are

5

people standing at

(0, 0)

(3, 0)

(0, 3)

(-3, 0)

, and

(-3, 0)

on a coordinate grid at a time

t = 0

seconds. Each second, every person on the grid moves exactly

1

unit up, down, left, or right. The person at the origin is infected with covid-

19

, and if someone who is not infected is at the same lattice point as a person who is infected, at any point in time, they will be infected from that point in time onwards. (Note that this means that if two people run into each other at a non-lattice point, such as

(0, 1.5)

, they will not infect each other.) What is the maximum possible number of infected people after

t = 7

seconds?
p4. Kara gives Kaylie a ring with a circular diamond inscribed in a gold hexagon. The diameter of the diamond is

2

mm. If diamonds cost

\$100/ mm ^2

and gold costs

\$50 /mm ^2

, what is the cost of the ring?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement