The Lady or the Tiger? A Famous Logic Puzzle

Here is a well-known conundrum that was quite controversial in its day. A lot of mathematicians couldn't even get the answer right! It looks deceptively simple...

The Lady or the Tiger

A young prince and princess had fallen in love, but the girl's father, a bitter old King, opposed the marriage. So the King contrived to lure the Prince into a trap. In front of his entire Court — nobles, clergy, jesters and even scullery-maids — he challenged the Prince to prove his love in a highly unusual and dangerous game.

"The Princess," said the King, "is behind one of these three doors I have placed in front of you. Behind the other two are hungry tigers who will most certainly eat you for dinner. If you prove your love by picking the correct door, you may marry my daughter!"

"And just to demonstrate that I'm not a bitter old man," said the King (who secretly suspected that's exactly what everyone thought of him), "I will help you. Once you make your choice, but before you open the door, I will show you a tiger behind one of the other doors. And then," intoned the King magnanimously, "you may pick again!"

The Prince knew that if he walked away he would likely be banished in shame from the Kingdom forever."

The court broke out into polite and dutiful applause. The King smiled, convinced that the Prince would not be man enough to take the challenge, even with the King's help.

Now the Prince knew that if he walked away he would likely be banished in shame from the Kingdom forever, never to see his love again. This he could not bear. And he was also a very clever Prince. So he swallowed hard, uttered a short prayer for luck, and then picked a door at random.

"I choose this door," said the prince in his deep, manly voice, as he walked over to one of the doors.

"Wait!" commanded the King in surprise. "I am as good as my word. Now I will show you a tiger. Guards! Reveal a tiger from behind one of the two remaining doors!"

Three of the Kings guards cautiously walked over to one of the other doors, opened it a crack, and then quick as they could slammed it shut. A huge hungry tiger had been crouching right behind it! The door shook as the tiger leaped up against it.

"Now," said the King, "Make your choice!" And, glancing to his court, he added, "Unless of course you wish to give up now and walk away..."

What Are the Prince's Chances?

The prince is now left with two doors. Behind one of them is a tiger, and behind the other is the Princess. Should he stick with the original door he picked, or open the other one? Or does it even matter? And what are his chances of living happily ever after with the Princess?

Hint: Even though he has two doors left, his chances are actually NOT 50/50.

If you think you know the solution or are stuck, you can read the Lady or Tiger answer here. You can also email me at mazes for more of an explanation.

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A simply-connected maze has pathways that never re-connect with one another, so every path either leads to additional paths (a fork) or to a dead end.

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The Lady or the Tiger? A Famous Logic Puzzle