Interview

There is a book with N pages (indexed from 1 to N). Each page has a certain number of words.
Now play a game with a player machine. Every time you send a message to it, the message contains the information "the sum of words in pages from i to j (1 <= i <= j <= N) is odd or even". The player can save this information and check whether the coming message has conflict with the information from ALL the previous messages. If so, return false and the game ends. If there is no conflict, save this information and return true.

Example:
  Game one:
     [3, 5, odd] -> true
     [6, 8, even] -> true
     [3, 8, even] -> false
  Game Two:
     [2, 10, odd] -> true
     [8, 14, even] -> true
     [2, 14, even] -> true
     [8, 10, even] -> false