Brain-Twisters IV

The puzzles in this page will generally be examples of the categories I enjoy most - those involving geometry, topology, probability, and truth paradoxes. Presenting them will often involve the use of tables and figures. The page should still be readable with text-based browsers such as Lynx, provided the reader has some way of downloading and viewing gif figures.

Puzzle #1

Based on the e-mail response, the classic "Lady or the Tiger" puzzles appear to be consistently popular. Here, without further ado, are three new ones.

There are now three rooms to choose from. Only one contains a lady while the other two contain tigers. The signs on the doors of the three rooms are as follows:

I

A TIGER IS IN THIS ROOM

 II

A LADY IS IN THIS ROOM

 III

A TIGER IS IN ROOM II

At most one of the three signs is true. Which room contains the lady?

Solution.

Puzzle #2

Once again, there are three rooms, containing yet again one lady and two tigers. The signs on the doors of the rooms this time are:

I

A TIGER IS IN ROOM II

 II

A TIGER IS IN THIS ROOM

 III

A TIGER IS IN ROOM I

The sign on the door of the room containing the lady is true, but at least one of the other two signs is false. What should your choice be?

Solution.

Puzzle #3

You are again faced with three rooms. However, this time one of the three rooms contains a lady, another a tiger, and the third room is empty. The signs on the doors of the rooms are:

I

ROOM III IS EMPTY

 II

THE TIGER IS IN ROOM I

 III

THIS ROOM IS EMPTY

Given that the sign on the door of the room containing the lady is true, the sign on the door of the room with the tiger is false, and the sign on the door of the empty room can either true or false, can you determine which room contains the lady? Can you also determine which room contains the tiger?

Solution.

Puzzle #4

Readers might recall the puzzle from last month in which they were asked to show that the ratio of the areas between two triangles, one of which was inscribed in a circle that was itself inscribed in the other triangle, was indeed four to one.

This is a similar puzzle. The triangle is, of course, an equilateral one. Once again, without indulging in any terribly complicated mathematics, determine the ratio between the areas of the two circles.

Download this figure for Puzzle #4.

Solution.

Puzzle #5

Two proof readers are checking two copies of the same manuscript. The first finds thirty errors, and the second finds only twenty-four. When their completed proofs are compared, it turns out that only twenty errors have been spotted by both of them.

How many errors would you suspect remain, not detected by either of them?

Solution.

Visit:

Puzzles 1-3 adapted from Smullyan, R. (1982) The Lady or the Tiger? and Other Logic Puzzles, Knopf.
Puzzle 4 adapted from Gardner, M. (1981) Science Fiction Puzzle Tales, C. N. Potter.
Puzzle 5 adapted from Wells, D. (1992) The Penguin Book of Curious and Interesting Puzzles, Penguin.
Revised: January 6, 1997