Three Gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one God. The Gods understand English, but will answer all questions in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

1. It could be that some God gets asked more than one question (and hence that some God is not asked any question at all).
2. What the second question is, and to which God it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
3. Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
4. Random will answer “da” or “ja” when asked any yes-no question.

What would your three questions be?

A boy saw a shirt for \$97 but does not have enough cash. So he borrowed \$50 from his mom and another \$50 from his dad.

He bought the shirt, and got back \$3 as change. He gave his dad \$1 and his mom \$1 and kept the other \$1 for himself.

Now mom and dad paid \$10 each and got back \$1 each. So they paid \$49 each, totaling \$98. The boy has another \$1, adding up to \$99. Where is the missing dollar?

There is a house. One enters it blind and leaves it seeing. What is it?

A man lives on the twelfth floor of an apartment building. Every morning he takes the elevator down to the lobby and leaves the building. In the evening, he gets into the elevator, and, if there is someone else in the elevator or if it was raining that day, he goes back to his floor directly. Otherwise, he goes to the tenth floor and walks up two flights of stairs to his apartment that is on the twelfth floor. Why?