8.3. On the board, there are 7 natural numbers. Prove that one of them can be erased so that the sum of the remaining numbers is even.
(5-6 grades)
This one wants a proof. Work it on paper, read the official solution, then mark
yourself honestly — the ladder only means something if the record is true.
Official solution
8.3. Among seven natural numbers, there is an odd number of either even or odd numbers. One of them needs to be erased. Then, both the number of even and odd numbers left will be even. Therefore, the sum of them will be an even number.
Source: NuminaMath-1.5,
licensed Apache-2.0.
Statement and solution reproduced as published; topic, difficulty and ordering added
by this site.