MathDB

p7. An ant starts at the point

(0, 0)

. It travels along the integer lattice, at each lattice point choosing the positive

x

y

direction with equal probability. If the ant reaches

(20, 23)

, what is the probability it did not pass through

(20, 20)

?
p8. Let

a_0 = 2023

and

a_n

be the sum of all divisors of

a_{n-1}

for all

n \ge 1

. Compute the sum of the prime numbers that divide

a_3

.
p9. Five circles of radius one are stored in a box of base length five as in the following diagram. How far above the base of the box are the upper circles touching the sides of the box? https://cdn.artofproblemsolving.com/attachments/7/c/c20b5fa21fbd8ce791358fd888ed78fcdb7646.png
PS. You should use hide for answers. Collected [url=https://artofproblemsolving.com/community/c5h2760506p24143309]here.

Problem Statement