13

Part of 2021 MOAA

Problems(2)

Source:

30

identical unit cubes. He can join two cubes together by gluing a face on one cube to a face on the other cube. He must join all the cubes together into one connected solid. Over all possible solids that Bob can build, what is the largest possible surface area of the solid?
Proposed by Nathan Xiong

Source:

Determine the greatest power of

2

that is a factor of

3^{15}+3^{11}+3^{6}+1

.
Proposed by Nathan Xiong