Particularly, I am not quite understanding why one of the values can’t be higher than the original average, as long as it is not higher than the new average?

Thanks for your reply. I understand the concept behind your explanation, but I was thinking in the particular question, if the original average is 77, couldn’t there be a situation where the lowest three numbers are 0, 54, and 78, and all of the other nine numbers are 88 (the new average)?