Another Clever Riddle

[mithrandir]

Let me ask you all something.  You know the rules...if you know the answer, please don't post it.  But I promise you I will post the answer within one week (unless I get run over by a freight train or win a vacation to Antarctica).

You're walking through the woods, and you only have one match.  You come to a log cabin.  Inside is a candle, a wood-burning stove and a lantern.  What do you light first?

mithrandir

[outdeep]

Oh, come on, Clarence.  That one is easy.  You first light the golden lampstand.  

[al Hartman]

Clarence,

     That's IT?!   i need more input:  Is the cabin unlocked?  Is anyone at home?  How long do i have until sunset?  Is this cabin in the northern or southern hemisphere?  Are there bears in the woods?  Is the pope a catholic?

  al

[mithrandir]

Okay, okay, the riddle wasn't that hard, I guess.  You light the match first.

mithrandir

[Eulaha L. Long]

Mr. and Mrs. Mustard have six daughters and each daughter has one brother. How many people are in the Mustard family?

[Kimberley Tobin]

NINE  

[Joe Sperling]

I'm not sure how many are in the Mustard family, but they all relish one another, and they're sure to help each other out if they get in a pickle. Lettuce think about that and do the same. Beets me why I like puns so much.

[delila]

And let's hope they serve Canadian beef at the table with them there condiments.

Moo!      Get out of here, cow!  What are you, crazy?



drj

[jesusfreak]

How many squares are on a chessboard?  

--
lucas

[sfortescue]

I have a chessboard that has only 32 squares.

They are slightly smaller than the spacing so that their edges don't join to make continuous lines across the board.  Also, since the board is folded up in its box, the outer border doesn't make a square either.

[Scott McCumber]

I have a chessboard that has only 32 squares.

They are slightly smaller than the spacing so that their edges don't join to make continuous lines across the board.  Also, since the board is folded up in its box, the outer border doesn't make a square either.

Funny. But what about a regular chess board?

[al Hartman]

I'm not sure how many are in the Mustard family, but they all relish one another, and they're sure to help each other out if they get in a pickle. Lettuce think about that and do the same. Beets me why I like puns so much.

     I keep hoping to get the jump on Joe one of these times, but he's too quick -- I guess I'll never ketchup.  Then again, the opportunity may turnip.  I'd probably be more motivated if I received a celery for my efforts.  Orange you glad you read this thread?

[d3z]

How many squares are on a chessboard?

Unless this is a trick question (so not counting pieces, players, or decorations), I get 204.

[Scott McCumber]

How many squares are on a chessboard?

Unless this is a trick question (so not counting pieces, players, or decorations), I get 204.

That's what I get.

How many rectangles? Similar formula but now your adding 1x1;1x2;1x3 . . . ;2x1;2x2; . . . ;8x1;8x2 . . .

[sfortescue]

The number of rectangles in a rectangle is a(a+1)b(b+1)/4.

The number of squares in a rectangle is a(a+1)(3b-a+1)/6, where a<=b.


How about harder questions:

A. How many 8 by 8 mazes are there?

B. How many ways can a chessboard be cut up into 32 dominos?

C. How many ways can a hexagon be cut up into unit rhombuses?


Answers:

A: 126231322912498539682594816

B: 12988816

C: For a hexagon with sides a, b and c:

the # of tilings = product(n^e_n)

where sum(e_n x^n) = (x^a - 1)(x^b - 1)(x^c - 1) x/(x-1)^2.