The Figure 8 Puzzle

figure 8 puzzle

Can this loop of string be freed from its wire? Stewart Coffin, who devised the puzzle in 1974, writes, “I soon became convinced that this was impossible, but being a novice in the field of topology, I was at a loss for any sort of formal proof.” He published the challenge in a newsletter and has been receiving requests for a solution ever since. Adding to the confusion, in 1976 a British puzzle editor mistakenly claimed with that Coffin’s creation was equivalent to another puzzle with a known solution, and Pieter van Delft and Jack Botermans published an amusingly bewildering “solution” of their own in their 1978 book Creative Puzzles of the World.

In the meantime, fans around the world have continued to experiment, and mathematicians Inta Bertuccioni and Paul Melvin have both offered proofs that the puzzle is unsolvable. “Whoever would have guessed that this little bent piece of scrap wire and loop of string would launch itself on an odyssey that would carry it around the world?” Coffin writes. “Will it mischievously rise again, perhaps disguised in another form, as topological puzzles so often do?”

Odd and Even

A puzzle by Noboyuki Yoshigahara:

“An odd number plus an odd number makes an even number. An even number plus an odd number makes an odd number. An even number plus an even number is an even number. Right?”


“An odd number times an odd number is an odd number. An even number times an odd number is an even number. Right?”


“An even number times an even number is an odd number. Right?”


“You don’t think so? An even number times an even number is an odd number.”


Click for Answer

Circles and Squares

circles and squares 1

Here are three circles and two squares, inscribed successively as shown.

If the diameter of the largest circle is 10, what is the diameter of the smallest circle?

Click for Answer

Four in Three

four in three

Can a square be inscribed in any triangle?

Click for Answer

“A Tradesman in a Difficulty”

A puzzle by Angelo Lewis, writing as “Professor Hoffman” in 1893:

A man went into a shop in New York and purchased goods to the amount of 34 cents. When he came to pay, he found that he had only a dollar, a three-cent piece, and a two-cent piece. The tradesman had only a half- and a quarter-dollar. A third man, who chanced to be in the shop, was asked if he could assist, but he proved to have only two dimes, a five-cent piece, a two-cent piece, and a one-cent piece. With this assistance, however, the shopkeeper managed to give change. How did he do it?

Click for Answer


From the 2000 Indiana College Mathematics Competition:

Four suspects, one of whom was known to have committed a murder, made the following statements when questioned by police. If only one of them is telling the truth, who did it?

Arby: Becky did it.
Becky: Ducky did it.
Cindy: I didn’t do it.
Ducky: Becky is lying.

Click for Answer

The Five Rooms

five rooms

Here’s the floor plan of a house with five rooms. Can you draw a continuous line that passes through each of the 16 wall segments once and once only? If it’s possible, show how; if it’s not, explain why.

Click for Answer