MathDB

Set 6
p16. Let

x

and

y

be non-negative integers. We say point

(x, y)

is square if

x^2 + y

is a perfect square. Find the sum of the coordinates of all distinct square points which also satisfy

x^2 + y \le 64

.
p17. Two integers

a

and

b

are randomly chosen from the set

\{1, 2, 13, 17, 19, 87, 115, 121\}

, with

a > b

. What is the expected value of the number of factors of

ab

?
p18. Marnie the Magical Cello is jumping on nonnegative integers on number line. She starts at

0

and jumps following two specific rules. For each jump she can either jump forward by

1

or jump to the next multiple of

4

(the next multiple must be strictly greater than the number she is currently on). How many ways are there for her to jump to

2022

? (Two ways are considered distinct only if the sequence of numbers she lands on is different.)
PS. You should use hide for answers.

Problem Statement