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Old 8/23/05, 08:03 AM
  #61  
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Originally posted by SurfnSoCal@August 22, 2005, 5:30 PM
ok, and one more to keep everyone busy who got the first one:

While on your interplanetary vacation, you decide to stop at the planet Quocorri, a planet known for its many mathematical achievements.

While there, you decide to pick up on some of the Quocorrians mathematical variations. The Quocorrians won't tell you exactly how it works, only that it has some relationship to the Standard English math. They also give you four, true, Quocorrian math problems. They are:

2+2=9
4*1=1
5-2=16
-3+2=64

So, according to this system, what is 6/2?
81
Old 8/23/05, 11:11 AM
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thats correct now someone answer the lewis carroll one before we move on
Old 8/23/05, 12:05 PM
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Originally posted by Enfynet@August 22, 2005, 10:59 AM
We have a... um... multiple winners!

Ok, more fun...
Lewis Carroll- Pillow Problem #8:
Some men sat in a circle, so that each had 2 neighbors; and each had a certain number of shillings. The first had one shilling more than the second, who had one shilling more than the third, and so on. The first gave one shilling to the second, who gave two to the third, and so on, each giving one shilling more than he recieved, as long as possible. There were two neighbors, one of whom had 4 times as much as the other. How many men were there? And how much did the poorest man start with?
There are 7 men, the poorest started with 2 shillings.
Old 8/23/05, 01:39 PM
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ok now all of them are solved, is anyone interested in explainations on any of them or should we just move on?
Old 8/23/05, 08:13 PM
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I've spent all of 5 mins on that math one... My manager at work spent 3 sheets of paper on it and came up with like 5 different answers. I'm sure I'll figure it out eventually... Meanwhile um...


Diophantus' Riddle:
Diophantus' youth lasted 1/6 of his life. He grew a beard after 1/12 more of his life. After 1/7 more of his life, he married. Five years later he had a son. His son lived exactly 1/2 as long as his father, and Diophantus died just four years after his son. How old was Diophantus when he died?
Old 8/23/05, 10:45 PM
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let x=Diophantus' age
let y=Diophantus' son's age

(1/6+1/12+1/7)x+5+y+4
and
y=x/2

solve for both and
Diophantus was 84 and his son was 42
Old 8/23/05, 11:56 PM
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I just used L

1/6L + 1/12L + 1/7L + 5 + 1/2L + 4 = L

So I got
L - 1/2L - 1/6L - 1/12L - 1/7L = 9
3/28L = 9
L = 3x28 = 84

Edit:
Diophantus' youth lasted 1/6 of his life. = 14
He grew a beard after 1/12 more of his life. = 21
After 1/7 more of his life, he married. = 33
Five years later he had a son. = 38
His son lived exactly 1/2 as long as his father, (42) = 80
and Diophantus died just four years after his son. = 84

Someone else post another one... I'm running out.
Old 8/24/05, 12:50 AM
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ok heres one......

If you paint the faces of a cube with six different colors, how many ways are there to do this if each face is painted a different color and two colorings of the cube are considered equivalent if you can rotate one to get the other? What if we drop the restriction that the faces be painted different colors?
Old 8/24/05, 08:33 AM
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Originally posted by rrobello@August 24, 2005, 12:53 AM
ok heres one......

If you paint the faces of a cube with six different colors, how many ways are there to do this if each face is painted a different color and two colorings of the cube are considered equivalent if you can rotate one to get the other? What if we drop the restriction that the faces be painted different colors?
The total different ways it can be painted before taking into account rotating the cube is 6! = 6*5*4*3*2*1 = 720. Now a cube can be rotated into 24 different positions. so 720/24 = 30.

Dropping color restrictions, 6*6*6*6*6*6 = 46656, then cancelling out the duplicates by rotating, 46654/24 = 1944.
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