
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. 
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. 
Is it possible to construct the fraction 1/2 by summing other fractions of the form 1/x^{2}? For example, you can choose various denominators as in: 1/3^{2} + 1/5^{2} + 1/10^{2} + ... (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.
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: 639,172^{2} = 408,540,845,584
Can you find the only other sixdigit 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.
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:
1) What is the first and second prime number we encounter on this triangle? 2) What percentage of prime numbers do you expect as we scan more rows in the mysterious triangle? 3) If you could add one digit to the beginning of each number in order to increase the number of primes, what would it be? Justify your answer. 4) If you could add one digit to the end of each number in order to increase the number of primes, what would it be? Justify your answer. 5) What is the largest prime number in this progression known to humanity? 6) You get to ask the angel a fascinating question about this triangle. What is your question? (You get extra points if you can give a good answer to your new question. Be creative.)
Some mind boggling answers here. What can you add to our findings?
Click here for several "alien gift"
puzzles
that test our thoughts about giving, beauty, and fear.
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
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. 