Posted: Thu Jun 29, 2006 5:14 pm
HINT: you have to remeber your geomerty proofs #81 Three cards, each with a positive integer written on it, are lying face-down on a table.
Jennifer, Brian, and Ed are told that:
a) the numbers are all different
b) they sum to 13, and
c) they are in increasing order, left to right
First, Jennifer looks at the number on the leftmost card and says, "I dont have enough information to determine the other two numbers."
Then, Ed looks at the number on the rightmost card and says, "I dont have enough information to determine the other two numbers."
Finally, Brian looks at the number on the middle card and says, "I dont have enough information to determine the other two numbers."
The three people are perfect logicians and always tell the truth, and know that they are all perfect logicans and always tell the truth. They all hear what the others are saying.
What is the number on the middle card?(7 points)
#84 Write a 10-digit number. The first digit tells how many zeroes there are in the number. The second digit tells how many ones that are in the number. The third digit tells how many twos there are in the number, and so on. The last number tells how many nines there are in the number. What is this number?(7)
#85 What name has three "A"s in it where each has a different sound?(4)
#86 If a rooster is perched on the top of a barn with the barn roof sloping east and west, and just as the sun rises the rooster lays an egg, on which side of the barn will the egg roll?(4)
#87 Four people are suspected of stealing a diamond from a museum. If one of their statements are true, and one is false, who is the thief?
Bo said: It was Bo. It wasn't Roman.
Roman said: It was Kate. It wasn't Bo.
John said: It was Roman. It wasn't Kate.
Kate said: It was John. It was Bo.
(4)
Score leaders
Kingwaffles - 87
johnnyrotten - 59
resitnecdan - 19
gadgetguy - 18
heavycola - 16
wicked - 15
risk06 - 14
reverend_kyle - 13.5
qeee1 - 13
Evil pope - 11
birdzs_lover - 10
hawkeye - 10
Mr. Dexter - 9
Subi - 9
Kernal_Kronic - 8
Phobia - 7
JCole200 - 6
Mach - 6
Highborn - 5.5
TitusFinn - 5.5
Koolbak - 3
#77 I have 2 books on the bookshelf, standing side by side, just like the books in a bookstore. The book on the right would have had twice as many pages as the book on the left, if only the book on the left had 5 more pages than it does now. The number of pages in the book on the right is not only a perfect square, but a perfect cube as well, and is less than 500.
A bookworm starts eating at the front cover of the book on the left (Eating it), and eats all the way through the last page of the book on the right (Eating it as well). How many pages did the bookworm eat?
(5)resitnecdan + risk
#78 You have committed some terrible crime, and the US government has imprisoned you in a very odd type of prison. There are 61 cells, numbered -30 to 30, all in a line, with doors in between them and exit doors on the outsides of cell -30 and 30. You are placed in cell #0, and every day they flip a (fair) coin and, based on the flip, open one door or another, and you must walk through it. Therefore, on day 1, you will either move to cell -1 or 1. Eventually, as days, weeks, and months go by, you will be in either cell -30 or 30, and if the coin flip ends up that you must move to cell -31, or cell 31, you are set free. You have no choice, you walk randomly back and forth based on the coin flip.
Visually, the cells look something like:
Freedom<-- [-30][-29][-28]...[-2][-1][0][1][2]...[28][29][30] -->Freedom
Now, for the question... What is more likely:
a) You get out on day 31
b) You get out on day 310
c) You get out on day 3100
(3)
resitnecdan
#82 If PORT is written as TSVX, which word is written as KMZI?(6)
risk
#83 Put a symbol between 2 and 3 to get a number bigger than 2 and smaller than 3.(4)risk
Jennifer, Brian, and Ed are told that:
a) the numbers are all different
b) they sum to 13, and
c) they are in increasing order, left to right
First, Jennifer looks at the number on the leftmost card and says, "I dont have enough information to determine the other two numbers."
Then, Ed looks at the number on the rightmost card and says, "I dont have enough information to determine the other two numbers."
Finally, Brian looks at the number on the middle card and says, "I dont have enough information to determine the other two numbers."
The three people are perfect logicians and always tell the truth, and know that they are all perfect logicans and always tell the truth. They all hear what the others are saying.
What is the number on the middle card?(7 points)
#84 Write a 10-digit number. The first digit tells how many zeroes there are in the number. The second digit tells how many ones that are in the number. The third digit tells how many twos there are in the number, and so on. The last number tells how many nines there are in the number. What is this number?(7)
#85 What name has three "A"s in it where each has a different sound?(4)
#86 If a rooster is perched on the top of a barn with the barn roof sloping east and west, and just as the sun rises the rooster lays an egg, on which side of the barn will the egg roll?(4)
#87 Four people are suspected of stealing a diamond from a museum. If one of their statements are true, and one is false, who is the thief?
Bo said: It was Bo. It wasn't Roman.
Roman said: It was Kate. It wasn't Bo.
John said: It was Roman. It wasn't Kate.
Kate said: It was John. It was Bo.
(4)
Score leaders
Kingwaffles - 87
johnnyrotten - 59
resitnecdan - 19
gadgetguy - 18
heavycola - 16
wicked - 15
risk06 - 14
reverend_kyle - 13.5
qeee1 - 13
Evil pope - 11
birdzs_lover - 10
hawkeye - 10
Mr. Dexter - 9
Subi - 9
Kernal_Kronic - 8
Phobia - 7
JCole200 - 6
Mach - 6
Highborn - 5.5
TitusFinn - 5.5
Koolbak - 3
#77 I have 2 books on the bookshelf, standing side by side, just like the books in a bookstore. The book on the right would have had twice as many pages as the book on the left, if only the book on the left had 5 more pages than it does now. The number of pages in the book on the right is not only a perfect square, but a perfect cube as well, and is less than 500.
A bookworm starts eating at the front cover of the book on the left (Eating it), and eats all the way through the last page of the book on the right (Eating it as well). How many pages did the bookworm eat?
(5)resitnecdan + risk
#78 You have committed some terrible crime, and the US government has imprisoned you in a very odd type of prison. There are 61 cells, numbered -30 to 30, all in a line, with doors in between them and exit doors on the outsides of cell -30 and 30. You are placed in cell #0, and every day they flip a (fair) coin and, based on the flip, open one door or another, and you must walk through it. Therefore, on day 1, you will either move to cell -1 or 1. Eventually, as days, weeks, and months go by, you will be in either cell -30 or 30, and if the coin flip ends up that you must move to cell -31, or cell 31, you are set free. You have no choice, you walk randomly back and forth based on the coin flip.
Visually, the cells look something like:
Freedom<-- [-30][-29][-28]...[-2][-1][0][1][2]...[28][29][30] -->Freedom
Now, for the question... What is more likely:
a) You get out on day 31
b) You get out on day 310
c) You get out on day 3100
(3)
resitnecdan
#82 If PORT is written as TSVX, which word is written as KMZI?(6)
risk
#83 Put a symbol between 2 and 3 to get a number bigger than 2 and smaller than 3.(4)risk
