Puzzles

 Mobius puzzles:   I am currently collecting puzzles for a book that involves Mobius strip puzzles. If you have any nice puzzles, like Mobius mazes and other Mobius curiosities, please contact me. Omniscience and God:   I discuss many religious puzzles in my new book The Paradox of God and the Science of Omniscience.

## Tunnels of Callicrates

 You and an alien are playing a game that involves a set of tunnels. The top of the map is North. In the game, you start at the entrance to the tunnels located at the top of this diagram. As you travel, you may only travel south, east, and west, but never North. Given these permitted directions, each time you have a choice of tunnels, you are equally likely to choose either route. You win a neural stimulator that gives you ecstatic pleasure if you emerge at the tunnel marked "Win." What is the likelihood that you will win the prize? (For this problem I want you to pretend you are a "mindless marble" always falling down or right or left (but not up). The marble keeps going until it reaches one of the four exits.) Some people think the chance of winning the prize is about 40%. Do you? Possible solution ideas are here, but we are, at present, uncertain of the most valid answer.

## Fragile Fractions

Is it possible to construct the fraction 1/2 by summing other fractions of the form 1/x2? For example, you can choose various denominators as in: 1/32 + 1/52 + 1/102 + ... (but this is not an answer!) The solution must have a finite number of terms. 1) Fragile Fractions of the 1st Kind: No value of x may be greater than 100. No values of x may be repeated. 2) Fragile Fractions of the 2nd Kind: you may use values greater than 100. Once you have found a solution for 1/2, can you construct a solution for: 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9? Click here for commentary and solutions.

## Exclusionary Squares and Cubes

I have a particular penchant for an unusual class of numbers called "exclusionary squares." Can you tell me what is so special about the number

639,172 ?

It turns out that this is the largest integer with distinct digits whose square is made up of digits not included in itself: 639,1722 = 408,540,845,584

Can you find the only other six-digit example? Can you find any exclusionary cubes? (I learned about exculsionary squares from my colleague Andy Edwards. So far, I am unaware of any large exclusionary cubes, and we may wish to generalize this to exclusionary numbers of the Nth order. I will report your "world records" in a forthcoming book.) Click here for commentary and solutions.

## Triangle of the Gods

An angel descends to Earth and shows the following simple progression of numbers:
```1
12
123
1234
12345
123456
1234567
12345678
... etc.
```
The angel will let you enter the afterlife if you can address 2 or more of the questions below in a satisfactory manner:

Some mind boggling answers here. What can you add to our findings?

## The Grand Internet Hunt for Obstinate Numbers

All you wanted to know about obstinate numbers.

## Extreme Challenges in Mathematics and Morals

A collection of problems and commentary on extreme problems.

that test our thoughts about giving, beauty, and fear.

## The Name Game Puzzle

How quickly can you find the name that does not belong? What methods did you use to find the name? What criteria did you use?

Piers Anthony Demi Moore Pamela Anderson Jenny McCarthy Cindy Crawford Alyssa Milano Alanis Morissette Claudia Schiffer Jennifer Connelly Sandra Bullock Jennifer Aniston Patricia Ford Madonna Selena Teri Hatcher Drew Barrymore Gillian Anderson Elle MacPherson Naomi Campbell Reiko Chiba Anna Nicole Smith Erika Eleniak James Bond Jimmy Buffett Humphrey Bogart Brad Pitt Jim Carrey Unabomber Rush Limbaugh George Michael Bruce Campbell Timothy Leary Hideo Nomo James Dean Piers Anthony Demi Moore Pamela Anderson Jenny McCarthy Cindy Crawford Alyssa Milano Alanis Morissette Claudia Schiffer Jennifer Connelly Sandra Bullock Jennifer Aniston Patricia Ford Madonna Selena Teri Hatcher Drew Barrymore Gillian Anderson Elle MacPherson Naomi Campbell Reiko Chiba Anna Nicole Smith Erika Eleniak James Bond Jimmy Buffett Humphrey Bogart Brad Pitt Jim Carrey Unabomber Rush Limbaugh George Michael Bruce Campbell Timothy Leary Hideo Nomo James Dean Piers Anthony Kathy Ireland Fiona Apple Demi Moore Pamela Anderson Jenny McCarthy Isaac Asimov Alyssa Milano Alanis Morissette Claudia Schiffer Jennifer Connelly Sandra Bullock Jennifer Aniston Patricia Ford Madonna Selena Teri Hatcher Drew Barrymore Gillian Anderson Elle MacPherson Naomi Campbell Reiko Chiba Anna Nicole Smith Erika Eleniak James Bond Jimmy Buffett Humphrey Bogart Brad Pitt Jim Carrey Unabomber Rush Limbaugh George Michael Bruce Campbell Timothy Leary Hideo Nomo James Dean Piers Anthony Kathy Ireland Fiona Apple Benoit Mandelbrot Benoit Mandelbrot Arthur C. Clarke Arthur C. Clarke Carl Sagan Carl Sagan Whitley Strieber Whitley Strieber Piers Anthony Kathy Ireland Fiona Apple Demi Moore Pamela Anderson Jenny McCarthy Cindy Crawford Alyssa Milano Alanis Morissette Claudia Schiffer Jennifer Connelly Sandra Bullock Jennifer Aniston Patricia Ford Madonna Selena Teri Hatcher Drew Barrymore Gillian Anderson Elle MacPherson Naomi Campbell Reiko Chiba Anna Nicole Smith Erika Eleniak James Bond Jimmy Buffett Humphrey Bogart Brad Pitt Jim Carrey Unabomber Rush Limbaugh George Michael Bruce Campbell Timothy Leary Hideo Nomo James Dean Benoit Mandelbrot Benoit Mandelbrot Arthur C. Clarke Arthur C. Clarke Carl Sagan Carl Sagan Whitley Strieber Whitley Strieber
As a reward, click here here to see a random image of one of the above individuals.

## Welcome to Worm World

Click on the above to see my puzzle involving weird worms.

## Mathematical Puzzles

Click on the above to see dozens of math puzzles,
including the infamous "Problem of the Bones."

## Eye Puzzle of the Week

Click on heading to see two eyes from a famous person. Can you guess who?

Not your average brain-benders. Plus my toughest puzzles yet.

## Grand Internet Math Challenge

Go beyond magic squares.

## The Antinoüs Prophecies

Solve an ancient mystery. Each one of the following nine prophecies refers to a historical event. Can you make a guess at the references? All of your past suggestions are cataloged in this new book, which also gives an explanation and background to these quatrains.

 1. After the skirmish, one is wounded the other dies.  The great white one sings by the fire of night.  The European does not rise but merely flies  Near the water, near the cross and knight. 2. An ape came from North, cool and damp  The stegosauri cry, poe, poe, loe.  My rear end hurts beneath the lamp  Thirty thousand opalescent hearts are low. 3. From the edge America, even as north,  A child, the rock, is born with an amber heart.  The change is nearly as the fourth:  Sea, land, a victory, and a cart. 4. The robber of the west, not of silver but gold  Places the caldron on darkening wine  Smoke is often less than sold  In a Latin furnace, like a hash, like a line. 5. Princess Charlene in Italy  With a trinity of peppers.  The white dove is a bee.  A hat does not hurt lepers. 6. The capuchin, covered with water  Some holy music, England, after a rain  Sees nothing but the bone daughter  And she, the long one, is in pain. 7. He will be betrayed by a lost friend,  He will leave through feigned desire,  She will be united twice until the end  Near the buildings, desert, and melted mire. 8 Lightning comes near the peninsula, and one will swim  There is ruin, Lester, but all is not lost  From the steel and silica brim  Blood, and water, but not at cost. 9 The dark head causes problems for the small king.  As much good as Asia, the winged, had done  There are the enemies, three, a ring,  The exiles scream, while J., the wires, do not shun.

## Pickover Discussion Group Puzzles

My friend Nick Hobson has collected some of the mathematical puzzles discussed in my Discussion Group into a great set of pages. Visit his site to see the collection.

Return to Cliff Pickover's home page which includes computer art, educational puzzles, higher dimensions, fractals, virtual caverns, JAVA/VRML, alien creatures, black hole artwork, and animations. Click here for a complete list of over 20 Cliff Pickover books.