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Logic to the Rescue

Ladies and Tigers - Puzzle #2

There once was a king in a far off land who read Frank Stockton's short story The Lady, or the Tiger?, in which a prisoner must choose between two rooms, one containing a lady and the other a tiger. If he chooses the former, the prisoner marries the lady; while if he chooses the latter, he (probably) gets eaten by the tiger.

Upon finishing this story, the king had an inspired flash. "That's the perfect way to try my prisoners!" he said to himself. "Only I won't leave anything 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 may win a nice bride to boot!"

Not one to delay, the king implemented his new policy the very next day.  Finding the previous problem easily solved by his prisoner, the king decided to change the rules a bit. He instructed his sign painter to prepare the following signs, and to place them on the doors in the arena.

Door 1
At least one room contains a lady.
Door 2
The other room contains a lady.

After this was done, the king had another prisoner marched in. He told him that the rooms might both contain tigers, they might both contain ladies, or one might contain a lady and the other a tiger. Additionally, if a lady was in Room 1, the sign on its door was true; while if a tiger was in Room 1, the sign on its door was false. The situation was just the opposite for Room 2.

Assume that you are the prisoner and want to find the lady, what would you do? Circle the action (1-5) that you would take. You must choose only one of them.

  1. open Door 1 as there is a tiger behind Door 2,
  2. open Door 2 as there is a tiger behind Door 1,
  3. open either door as there are ladies behind each,
  4. refuse to open either door as you know tigers are behind both,
  5. tell the king that he has not given you enough information to make a choice with absolute certainty

Use our three step logical problem solving procedure to prove that your choice alone meets all of the conditions specified by the king. Proofread your work for clarity, punctuation, spelling, capitalization, legibility, and conciseness.


The Solution

Possible solutions (the correct one is highlighted)

Possible solution 1

Room 1 - lady 
Room 2 - lady

Possible solution 2

Room 1 - tiger 
Room 2 - lady

Possible solution 3

Room 1 - lady 
Room 2 - tiger

Possible solution 4

Room 1 - tiger 
Room 2 - tiger

Fact list

  1. The sign on Door 1 is true if Room 1 contains a lady.
  2. The sign on Door 1 is false if Room 1 contains a tiger. 
  3. The sign on Door 2 is true if Room 2 contains a tiger.
  4. The sign on Door 2 is false if Room 2 contains a lady. 
  5. The sign on Door 1 says, "At least one room contains a lady."
  6. The sign on Door 2 says, "The other room contains a lady."

Evaluation (impossibilities are in bold)

  1. in possible solution 1, 
        the sign on Door 1 is TRUE 
        the sign on Door 2 is FALSE because room 2 contains a lady, but TRUE because room 1 contains a lady
  2. in possible solution 2, 
        the sign on Door 1 is TRUE because a lady is in room 2, but FALSE because room 1 contains a tiger
        the sign on Door 2 is FALSE
  3. in possible solution 3, 
        the sign on Door 1 is TRUE 
        the sign on Door 2 is TRUE
  4. in possible solution 4, 
        the sign on Door 1 is FALSE
        the sign on Door 2 is FALSE because a tiger is in room 1, but TRUE because a tiger is in room 2

Since solution #3 is the only one where both signs are consistent with all the facts, it must be correct.  As a prisoner, you'd select Door 1 and find a lady to marry.

This problem is an adaptation of one presented by mathematician Raymond Smullyan in his book, The Lady or the Tiger? And Other Logic Puzzles Including a Mathematical Novel That Features Godel's Great Discovery (Alfred A. Knopf, 1982).


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original web posting: Monday, June 4, 2001
last modified: Wednesday, July 26, 2006