Grammar Quiz #13 solicited some imaginative guesses, including one from Marie Gray who deserves honorable mention for her guess that maybe there should be another subject in the second half, or a comma. Actually, the problem is with the word, “alternate.” The word means ‘by turns’ or ‘every other.’ What we need here is a choice among options: “alternative.”
Dr. John’s Grammar Quiz #14 Can you eagle-eyed writers spot the glaring grammatical error in this sentence? “They knew that if they could have somehow played the first half the way they played the second half, they may have won.”
WriterCare with Dr. John 
The word “may” should be “might” in order to agree with the past tense.