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Puzzles
#1
Posted 2006-July-10, 10:55
What kind do you like? Can we have a go at some?
Here is one from Martin Gardner:
You have an 8x8 mutilated chessboard: a1 and h8 have been removed (the two end squares of the diagonal). You are given 31 dominoes (2x1 rectangles), can you cover the mutilated chessboard with those 31 dominoes completely?
Here is one from Martin Gardner:
You have an 8x8 mutilated chessboard: a1 and h8 have been removed (the two end squares of the diagonal). You are given 31 dominoes (2x1 rectangles), can you cover the mutilated chessboard with those 31 dominoes completely?
#4
Posted 2006-July-12, 05:47
This is a sort of puzzle...
Name a US state that is two antonyms separated by one letter. (Example: BlackQWhite)
Sean
Name a US state that is two antonyms separated by one letter. (Example: BlackQWhite)
Sean
#5
Posted 2006-July-12, 06:20
Answer hidden:
Another domino one: how many different ways are there of tiling a 2 by n board with n dominoes? (ignoring the pips on the dominoes)
Spoiler
Another domino one: how many different ways are there of tiling a 2 by n board with n dominoes? (ignoring the pips on the dominoes)
#6
Posted 2006-July-12, 07:29
I liked this one:
You are given 9 black marbles, 11 red marbles and 13 white marbles.
You are also given a magic device with a hole at the top and a dispenser at the bottom that works as follows:
How can that be done, if at all? If not, why not?
--Sigi
Hint (hidden):
You are given 9 black marbles, 11 red marbles and 13 white marbles.
You are also given a magic device with a hole at the top and a dispenser at the bottom that works as follows:
- if you insert two marbles of different color, the box eats the marbles and dispenses two marbles of the remaining color (eg. insert a red and a white, get two blacks in return etc.)
- if you insert two marbles of the same color, the box eats the marbles and dispenses two marbles, one of each remaining color (eg. insert two blacks and get one red and one white in return etc.).
- the box has an endless power supply, ie. it does the above as often as you want
How can that be done, if at all? If not, why not?
--Sigi
Hint (hidden):
Spoiler
#8
Posted 2006-July-12, 08:18
here are a couple of old ones... not hard, just old
a farmer has a hound, a fox, and a hen... he has to get himself and all 3 animals across a river, but his boat is so small that it will only hold him and one animal at a time... he can't leave the fox and hen alone, the fox will eat the hen... if he leaves the hound and fox alone, the hound will kill the fox... how does he cross the river with his 3 animals? like i said, not hard just old
the other relatively easy one goes like this (hope i remember it correctly)... there is a room that contains two doors... nothing distinguishes the doors, the only difference is that one door leads to heaven, the other to hell... the room also has in it two men, exact twins... they are the same in every way except that one always tells the truth and one always lies... they also happen to know which door leads to heaven and which to hell
you can ask either twin one and only one question... what question do you ask to determine which door leads to heaven?
a farmer has a hound, a fox, and a hen... he has to get himself and all 3 animals across a river, but his boat is so small that it will only hold him and one animal at a time... he can't leave the fox and hen alone, the fox will eat the hen... if he leaves the hound and fox alone, the hound will kill the fox... how does he cross the river with his 3 animals? like i said, not hard just old
the other relatively easy one goes like this (hope i remember it correctly)... there is a room that contains two doors... nothing distinguishes the doors, the only difference is that one door leads to heaven, the other to hell... the room also has in it two men, exact twins... they are the same in every way except that one always tells the truth and one always lies... they also happen to know which door leads to heaven and which to hell
you can ask either twin one and only one question... what question do you ask to determine which door leads to heaven?
"Paul Krugman is a stupid person's idea of what a smart person sounds like." Newt Gingrich (paraphrased)
#9
Posted 2006-July-12, 12:15
Blofeld, on Jul 12 2006, 07:20 AM, said:
Another domino one: how many different ways are there of tiling a 2 by n board with n dominoes? (ignoring the pips on the dominoes)
Hidden:
Spoiler
#11
Posted 2006-July-12, 13:24
How about this one (ridiculously hard):
What is the maximum number of completely bounded volumes that can be formed by three interpenetrating cubes, considering only the surfaces of the cubes as boundaries and counting only volumes that are not further subdivided?
(BTW I don't know the answer but it's supposed to have been posted somewhere on the net.)
--Sigi
What is the maximum number of completely bounded volumes that can be formed by three interpenetrating cubes, considering only the surfaces of the cubes as boundaries and counting only volumes that are not further subdivided?
(BTW I don't know the answer but it's supposed to have been posted somewhere on the net.)
--Sigi
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