I like neither of the two books.Please showme (a third) one.这里为什么要填a third?

the +序数词 意思为“第几.”
a +序数词 意思为“再次”（其含义为,在前面已经出现的次数上再增加一次,并且此次可能不是最后一次）
举个例子：John failed the test twice.But he would like to have a third try.
约翰俩次考试都不及格,但是他想再考一次.