It was my sister Alice's birthday, and I had a present for her. As you know, Alice is a very intelligent girl, and as you also know I like presenting little problems. So I gave Alice three boxes, one wrapped in red, one in yellow and one in blue. In one box, I told her, is your birthday present; the other two are empty. "Now," I said, "you have to determine in which box is the present. You can ask me any number of questions answerable by yes or no, and I'll either answer them all truthfully, or else I'll lie each time." First, she asked if the present was in the yellow box. I answered her, yes or no. Then she asked if it was in the red box, and again I answered yes or no. And Alice, after some thought, knew which box contained the present. How?

So when she asked you if it was in the yellow box, you didn't say "Yes or no". You either said "Yes" or you said "No" but you're not telling us what your answer was. Is that right?

Yes that's right. My answer was either yes or no in each case, but you don't know which. Alice, of course, does.

The only way she would know which box contained the present is if you gave the same answer in both questions. "Yes, Yes" means you were lying and "No, No" means you were telling the truth, and in either case the present would be in the blue box. If you answered one "Yes" and one "No" (regardless of the order) it would be in one of the first two boxes, but Alice wouldn't know which one, since she doesn't know if you're lying or telling the truth.

Spot on, Gil Galad. Well-reasoned.