MathDB

p19.

A_1A_2...A_{12}

is a regular dodecagon with side length

1

and center at point

O

. What is the area of the region covered by circles

(A_1A_2O)

(A_3A_4O)

(A_5A_6O)

(A_7A_8O)

(A_9A_{10}O)

, and

(A_{11}A_{12}O)

(ABC)

denotes the circle passing through points

A,B

, and

C

.
p20. Let

N = 2000... 0x0 ... 00023

be a

2023

-digit number where the

x

is the

23

rd digit from the right. If

N

is divisible by

13

, compute

x

.
p21. Alice and Bob each visit the dining hall to get a grilled cheese at a uniformly random time between

12

PM and

1

PM (their arrival times are independent) and, after arrival, will wait there for a uniformly random amount of time between

0

and

30

minutes. What is the probability that they will meet?
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement