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Logic to the Rescue

Ladies and Tigers - Puzzle #1

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. The arena was prepared, and the following signs placed on the two doors.

Door 1
Either a tiger is in this room,
or a lady is in the other room.
Door 2
A lady is in the other room.

After a prisoner was marched in, the king explained the ground rules. There could be ladies in both rooms, tigers in both rooms, or a lady in one room and a tiger in the other. Additionally, the signs on the doors were either both true or both false. Lastly, when a statement has more than one part connected with OR, it is false only when all parts are false.

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: 
        a. Room 1 contains a tiger; OR 
        b. Room 2 contains a lady 
  2. The sign on Door 2 is true only when Room 1 contains a lady. 
  3. The signs are either both true or both false.
  4. The sign on Door 1 says, "Either a tiger is in this room, or a lady is in the other room."
  5. The sign on Door 2 says, "A lady is in the other room."

Evaluation

  1. in possible solution 1
        the sign on Door 1 is TRUE 
        the sign on Door 2 is TRUE
  2. in possible solution 2, 
        the sign on Door 1 is TRUE 
        the sign on Door 2 is FALSE
  3. in possible solution 3, 
        the sign on Door 1 is FALSE 
        the sign on Door 2 is TRUE
  4. in possible solution 4, 
        the sign on Door 1 is TRUE 
        the sign on Door 2 is FALSE

Since it is given that the signs are either both true or both false, the only situation consistent with the rules stated by the king is #1. It therefore must be correct.  As a prisoner you could choose either door 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