i'm just stuck and can't stop thinking of this one.. can anyone help me?
One piece of paper is cut into 8 pieces. We select X pieces from them and cut each into 8 pieces. We select again X pieces and cut each into 8 pieces…continue doing like this. So which of the following can be a possible number of pieces in total after cutting?
2003?
2004?
2005?
2006?
I need some help..
karura 8 - X + X*8 describes what happens after you take the first X number pieces and cut them into 8 pieces. "X*8" will allways be even, but if X is an odd number 8 - X will also be an odd number. Which means 8 - X + even number can be an odd number.
I'm not exactly sure what formula one would use to calculate the continued cutting X pieces of paper up though. But it will be up to the number of times you keep cutting up X pieces wether or not the number is odd or even.
(for examlple if X = 3 you first get 29 and after that 50 and after that 71, 92 etc etc
X=5 you get 43, 78, 113 etc)
hmmm 8-X + X*8 + X*7*(Y-1) where Y is the number of times you take X pieces of paper and cut them into 8.
Does that work sinu or what formula did you use? I'm sure there's a simpler one. But I haven't done this for some time and I kinda just woke up after a nap =P
I'm not exactly sure what formula one would use to calculate the continued cutting X pieces of paper up though. But it will be up to the number of times you keep cutting up X pieces wether or not the number is odd or even.
(for examlple if X = 3 you first get 29 and after that 50 and after that 71, 92 etc etc
X=5 you get 43, 78, 113 etc)
hmmm 8-X + X*8 + X*7*(Y-1) where Y is the number of times you take X pieces of paper and cut them into 8.
Does that work sinu or what formula did you use? I'm sure there's a simpler one. But I haven't done this for some time and I kinda just woke up after a nap =P
Crezax wrote:If you feel you need to write something angry and insulting, write it down in Notepad, save it somewhere and look at it when you get bored.
On the first round of cuts, you take x_1 number of pieces out of the original 8 and you cut those into 8. So in the first round you have a total of:
8 - x1 + 8*x1
= 8 + (8-1)*x1
= 8 + 7*x1
On the second round of cuts, you take x_2 number of pieces from what you had in the last round and then you cut those into 8 pieces. So then you have a total of:
8 + 7*x1 - x2 + 8*x2
= 8 + 7*x1 + (8-1)*x2
= 8 + 7*x1 + 7*x2
If you extrapolate, for xN number of rounds, you will have
8 + 7*x1 + 7*x2 + 7*x3 + ..... + 7*xN
Which has to equal one of the choices. Or, better yet, the following has to hold true:
8 + 7 * (x1 + x2 + x3 + ..... + xN) = 2003, 2004, 2005 or 2006
Since x1 + ... + xN has to be a whole number, then you're left with the only answer which is 2003.
8 - x1 + 8*x1
= 8 + (8-1)*x1
= 8 + 7*x1
On the second round of cuts, you take x_2 number of pieces from what you had in the last round and then you cut those into 8 pieces. So then you have a total of:
8 + 7*x1 - x2 + 8*x2
= 8 + 7*x1 + (8-1)*x2
= 8 + 7*x1 + 7*x2
If you extrapolate, for xN number of rounds, you will have
8 + 7*x1 + 7*x2 + 7*x3 + ..... + 7*xN
Which has to equal one of the choices. Or, better yet, the following has to hold true:
8 + 7 * (x1 + x2 + x3 + ..... + xN) = 2003, 2004, 2005 or 2006
Since x1 + ... + xN has to be a whole number, then you're left with the only answer which is 2003.
Does X stay the same each time? I'm confused about how to read that x1, x2, x3 stuff.
ugh I forgot all about that annoying N crap math... or perhaps i never really understood it in the first place.
ugh I forgot all about that annoying N crap math... or perhaps i never really understood it in the first place.
Crezax wrote:If you feel you need to write something angry and insulting, write it down in Notepad, save it somewhere and look at it when you get bored.
