Inspired by this question.
Two friends, Andrew and Gabriel are approached one day by their friend Harry.
"So, Ellen tells me you two can read each other's mind," says Harry.
"Yeah that's right," says Andrew. "Would you like us to demonstrate it to you?"
"Yes," says Harry, "but I'm a bit more skeptical than Ellen, so I'm not going to let you give the questions. Instead, you will whisper them to me and I will ask the questions. And just to make sure you aren't doing anything funny, I reserve the right to ask a different question than the one you ask me."
"But you might always change the question and never ask the thing we are really thinking about!" exclaims Andrew.
"All right, I'll tell you what," says Harry. "When one of you is ready to ask if it is the thing you are thinking about, whisper "5" into my ear before the word, and I won't change it. Is that okay?"
"Hmm, I don't know," says Gabriel. "Let us talk this over first." He whispers something to Andrew, Andrew shakes his head, and then whispers something back. Then they both nod and agree to the terms.
Andrew steps away from Gabriel and Andrew gets blindfolded and waits. Then Gabriel whispers something in the ear of Harry. Harry then says: "Ok, Gabriel is establishing the mental link, are you ready Andrew?"
"Yes I am" replies Andrew.
"Is it a rhinoceros?" asks Gabriel.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a Teletubby?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a rainbow?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it the Statue of Liberty?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a pumpkin?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it the Magna Carta?" asks Harry.
"Yes!" replies Andrew.
"Lucky guess," says Harry. "This time I'm going to tell Gabriel what it is you are guessing, and he will whisper the questions. Just in case you decided before hand what you were going to think about. Same as before, I might change any question beside the actual answer."
Harry whispers something into Gabriel's ear. Gabriel whispers something back in Harry's ear.
"Is it a candle?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it the color blue?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a Beautiful Sunshine of the Spotless Mind?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it Bart Simpson?" asks Harry.
"Yes!" replies Andrew.
"Hmm," says Harry. "Let's try this one more time." He again whispers something into Gabriel's ear. Gabriel whispers something back into Harry's ear.
"Is it chlorophyll?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a turnip in a field of donkeys?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it an avalanche in the Swiss Alps?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a wigwam on the prairie?" asks Harry?
"Yes!" replies Andrew.
At this point Harry suspects that Andrew and Gabriel are just waiting a fixed number of "no" answers, so he lets do another round to see if he is right. However, he does not let on as to his suspicions. He whispers another answer to Gabriel, and then Gabriel whispers something to Harry.
"Is it a clown?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it the North Pole?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it Julie Andrews?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it Pope Benedict the sixteenth?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a dead plant?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it Superman?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it... a lion? asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a bathtub?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a school bus?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a coal mine?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a Glade plug-in air freshener?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a wombat?" asks Harry.
"No," replies Andrew. Gabriel whispers something to Harry.
"Is it a baseball?" asks Harry.
"Yes!" replies Andrew.
"Huh," says Harry. "I guess you really can read minds."
Note: In the last round, Harry did not whisper any of the questions Gabriel asked, except of course for the last one.
Why is Harry wrong? If you think you know the answer, create a question/answer session for the next thing Harry is going to think of.
Hint:
Andrew and Gabriel are using a similar (but less fixed) mechanism as part 1.