Problem 1 (Taken from New York Times). Many of you are familiar with Frank Stockton's story "The Lady or the Tiger?

Problem 1 (Taken from New York Times). Many of you are familiar with Frank Stockton's story "The Lady or the Tiger?," in which the prisoner must choose between two rooms, one of which contains a lady and the other a tiger. If he chooses the former, he marries the lady; if he chooses the latter, he (probably) gets eaten by the tiger.

The king of a certain land had also read the story, and it gave him an idea. "Just the perfect way to try my prisoners!" he said one day to his minister. "Only, I won't leave it to chance; I'll have signs on the doors of the rooms, and in each case I'll tell the prisoner certain facts about the signs. If the prisoner is clever and can reason logically, he'll save his life ? and win a nice bride to boot!"

"Excellent idea!" said the minister.

On the first day, there were three trials. In all three, the king explained to the prisoner that each of the two rooms contained either a lady or a tiger, but it could be that there were tigers in both rooms, or ladies in both rooms, or then again, maybe one room contained a lady and the other room a tiger.

"Suppose both rooms contain tigers," asked the prisoner. "What do I do then?"

"That's your hard luck!" replied the king.

"Suppose both rooms contain ladies?" asked the prisoner.

"Then, obviously, that's your good luck," replied the king. "Surely you could have guessed the answer to that!"

"Well, suppose one room contains a lady and the other a tiger, what happens then?" asked the prisoner. "In that case, it makes quite a difference which room you choose, doesn't it?"

"How do I know which room to choose?" asked the prisoner.

The king pointed to the signs on the doors of the rooms:

I: IN THIS ROOM THERE IS A LADY, AND IN THE OTHER ROOM THERE IS A TIGER

II: IN ONE OF THESE ROOMS THERE IS A LADY, AND IN ONE OF THESE ROOMS THERE IS A TIGER

"Is it true, what the signs say?" asked the prisoner.

"One of them is true," replied the king, "but the other one is false.

" If you were the prisoner, which door would you open (assuming, of course, that you preferred the lady to the tiger)?

Problem 2. And so, the first prisoner saved his life and made off with the lady. The signs on the doors were then changed, and new occupants for the rooms were selected accordingly. This time the signs read as follows:

I: AT LEAST ONE OF THESE ROOMS CONTAINS A LADY

II: A TIGER IS IN THE OTHER ROOM

"Are the statements on the signs true?" asked the second prisoner.

"They are either both true or both false," replied the king. Which room should the prisoner pick?

3 Problem 3. In this trial, the king explained that, again, the signs were either both true or both false. Here are the signs:

I: EITHER A TIGER IS IN THIS ROOM OR A LADY IS IN THE OTHER ROOM

II: A LADY IS IN THE OTHER ROOM

Does the first room contain a lady or a tiger? What about the other room?