Hello World!
You want to determine whether a program P prints ”Hello World!” before running the kth line in the program. Is there a computer program that can perform this task?
Justify your answer.
2 Computability
There is no computer program Line which takes a program P, an input x, and a line number L, and determines whether the Lth line of code is executed when the program P is run on the input x.
3 Counting on Graphs
How many ways are there to color the faces of a cube using exactly 6 colors, such that each face has a different color? Note: two colorings are considered the same if one of them can be obtained by rotating the other.
4 Captain Combinatorial
Prove
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