(10pts) Alice got 1, 2, 3, . . . , 2023 a list of numbers as a birthday present (what a surprise!).
Alice doesnt like these numbers, so she wants to change them. At each change, Alice picks two
numbers from the list, say a and b, and removes them. Then, she inserts exactly one of the
numbers |a b| or a + b into the list (Note that the length of the list decreases by one after each
change). She stops when only one number is left on the list. Prove that the final remaining
number is even..
(10pts) Alice got 1, 2, 3, . . . , 2023 � a list of numbers � as a b.pdf
1. (10pts) Alice got 1, 2, 3, . . . , 2023 a list of numbers as a birthday present (what a surprise!).
Alice doesnt like these numbers, so she wants to change them. At each change, Alice picks two
numbers from the list, say a and b, and removes them. Then, she inserts exactly one of the
numbers |a b| or a + b into the list (Note that the length of the list decreases by one after each
change). She stops when only one number is left on the list. Prove that the final remaining
number is even.
