Archimedes' Bathtub

The Art and Logic of Breakthrough Thinking


These puzzles offer a kind of mental gymnasium for cultivating the art of breakthrough thinking.  Breakthroughs in thinking are made by recognizing subtle clues, challenging assumptions, and seeing old situations in new ways.  Many of our greatest inventions have been the result of breakthrough thinking.  Archimedes discovered how to measure the volume of an object in this way.  He had been working on the problem for awhile with no success.  One day while watching the water overflow the tub as he settled into it, the answer came in a snap:  The water displacement method was born.

These puzzles are actually from the book Archimedes' Bathtub, by David Perkins.  If you find the workings of the mind fascinating you'll love this book.  He explores the key processes behind breakthrough thinking and also how its been applied by great thinkers and inventors through the ages.  He also provides more than 50 puzzles throughout the book for you to play with.  You can get your own copy of this fascinating book at  This book is a very interesting read and will definitely change the way you look at problem solving.

You are driving a jeep through the Sahara desert.  You encounter someone lying face down in the sand, dead.  There are no tracks anywhere around.  There has been no wind for days to destroy tracks.  You look in a pack on the person's back.  What do you find?

The Extended Family
Four relatives spend a very pleasant day together catching up on old times.  Although there are just four of them, all by themselves they make up an extended family.  The four include a father and mother, a son and daughter, a sister and brother, an aunt and uncle, a niece and nephew, and two cousins.  All of these relationships occur within the group of four (the father is a father of someone else in the group, and so on.)  No marriages of people already relatives are involved.  How is this possible?

The Clock
One day a mantel clock that chimed the hours and quarter hours (one chime each quarter hour) struck twenty-seven times within the span of an hour and one minute.  Yet there was nothing wrong with the clock, and all this happened in a natural and appropriate way.  How could that be?

The Four Trees
A landscape architect has a passion for symmetry.  The designer decides to place four golden rain trees in a park so that each stands exactly the same sistance from all the others.  How does the landscape architect position the trees?

Pen Pals
Describe how you can put twenty-seven animals into four pens so that there is an odd number of animals in each pen.

The Cigarette Maker
A bum discovers that he can glue together five cigarette butts to make one cigarette.  Through assiduous effort, he scrounges up twenty-one cigarette butts.  How many full smokes does he get?

The Rope Ladder
A rope ladder hangs over the side of a boat near a dock.  The fifth rung is just under water.  The tide is risind at a steady rate of 1 foot per hour.  Each rung is 3/4 of an inch thick, and the gap from one rung to the next is 8 inches. How many rungs will be under water in 3 hours?