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Math Problem -- Grid Possibilities -- (TOUGH)

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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Bas » Sun 04 Nov 2007, 14:13:14

well, I did 11!/(5!*6!)....But I'm not sure...

wait...10!/(4!*6!) = 210...
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby idomar » Sun 04 Nov 2007, 14:14:58

either 666,

or four kajillion,

maths was never my forte, although if you turn it into a maze by colouring in some of the squares a-la fast food restaurant place mats, Ill happily have another stab at it.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby jasonraymondson » Sun 04 Nov 2007, 14:17:43

$this->bbcode_second_pass_quote('Bas', 'w')ell, I did 11!/(5!*6!)....But I'm not sure...

wait...10!/(4!*6!) = 210...



You are getting there

I am just not sure why you are using those number. This isn't a 24 square grid *hint
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Bas » Sun 04 Nov 2007, 14:25:56

well 14!/(10!*4!) = 1001....but that was wrong right?
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby dinopello » Sun 04 Nov 2007, 14:27:05

$this->bbcode_second_pass_quote('jasonraymondson', '')$this->bbcode_second_pass_quote('SteinarN', '1')001


nope


Are you sure? That's what I get.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby jasonraymondson » Sun 04 Nov 2007, 14:31:25

$this->bbcode_second_pass_quote('dinopello', '')$this->bbcode_second_pass_quote('jasonraymondson', '')$this->bbcode_second_pass_quote('SteinarN', '1')001


nope


Are you sure? That's what I get.


100% positive
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby jasonraymondson » Sun 04 Nov 2007, 14:36:29

$this->bbcode_second_pass_quote('Bas', 'w')ell 14!/(10!*4!) = 1001....but that was wrong right?


Yep, that is wrong. I have seen PMS logged on and he is suppose to be the math teacher, so I wonder why he hasn't answered the problem. This is only college algebra level stuff
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby dinopello » Sun 04 Nov 2007, 14:43:05

$this->bbcode_second_pass_quote('', 'T')his is only college algebra level stuff


I had Algebra in High School, maybe that's my problem.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Bas » Sun 04 Nov 2007, 14:43:07

$this->bbcode_second_pass_quote('jasonraymondson', '')$this->bbcode_second_pass_quote('Bas', 'w')ell 14!/(10!*4!) = 1001....but that was wrong right?


Yep, that is wrong. I have seen PMS logged on and he is suppose to be the math teacher, so I wonder why he hasn't answered the problem. This is only college algebra level stuff


Highschool where I'm from, but can't say this stuff is still fresh in my memory.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby jasonraymondson » Sun 04 Nov 2007, 15:18:41

Does everyone give up, or would you like more time. It is going to make you sick to see how close you were to the problem if I tell you.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Andrew_S » Sun 04 Nov 2007, 15:28:04

Why not wait until later, even tomorrow, to give others a chance?
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby MD » Sun 04 Nov 2007, 15:55:04

2nd hint:

There is one path that leaves 40 squares below the line.
There is one path that leaves 39 squares below the line.
there are two paths that leave 38 squares below the line.

....

There is one path that leave 40 squares above the line.
Stop filling dumpsters, as much as you possibly can, and everything will get better.

Just think it through.
It's not hard to do.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby MD » Sun 04 Nov 2007, 15:58:17

it's not linear
Stop filling dumpsters, as much as you possibly can, and everything will get better.

Just think it through.
It's not hard to do.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby jasonraymondson » Sun 04 Nov 2007, 17:46:23

$this->bbcode_second_pass_quote('MD', '2')nd hint:

There is one path that leaves 40 squares below the line.
There is one path that leaves 39 squares below the line.
there are two paths that leave 38 squares below the line.

....

There is one path that leave 40 squares above the line.


If you are claiming you know please send me the number of paths via pm.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby SteinarN » Sun 04 Nov 2007, 17:53:20

I'm pretty sure the right answer is 1001. I havent found a formula to get the answer, but i made a table. In the right upper corner there is only one alternative route, hence the numper one. In the field to the left from the right upper corner you have to go down to field 4 to have another path. From there it is 4 different paths to the lover left. In the field one mor to the left there is 10 different paths to the end. And so forth.
286+220+165+120+84+56+35+20+10+4+1=1001


_____________________________________________________
I1001_I_____I_____I_____I____I____I____I____I____I____I__1_I
I_286_I_220_I_165_I_120_I_84_I_56_I_35_I_20_I_10_I__4_I____I
I__66_I__55_I__45_I__36_I_28_I_21_I_15_I_10_I__6_I__3_I____I
I__11_I__10_I___9_I___8_I__7_I__6_I__5_I__4_I__3_I__2_I____I
I___1_I___1_I___1_I___1_I__1_I__1_I__1_I__1_I__1_I__1_I____I
Last edited by SteinarN on Sun 04 Nov 2007, 18:04:56, edited 1 time in total.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby dinopello » Sun 04 Nov 2007, 17:56:50

$this->bbcode_second_pass_quote('SteinarN', 'I')'m pretty sure the right answer is 1001. I havent found a formula to get the answer, but i made a table. In the right upper corner there is only one alternative route, hence the numper one. In the field to the left from the right upper corner you have to go down to field 4 to have another path. From there it is 4 different paths to the lover left. In the field one mor to the left there is 20 different paths to the end. And so forth.
286+220+165+120+84+56+35+20+10+4+1=1001


_____________________________________________________
I1001_I_____I_____I_____I____I____I____I____I____I____I__1_I
I_286_I_220_I_165_I_120_I_84_I_56_I_35_I_20_I_10_I__4_I____I
I__66_I__55_I__45_I__36_I_28_I_21_I_15_I_10_I__6_I__3_I____I
I__11_I__10_I___9_I___8_I__7_I__6_I__5_I__4_I__3_I__2_I____I
I___1_I___1_I___1_I___1_I__1_I__1_I__1_I__1_I__1_I__1_I____I


Exactly.

*____1____1____1____1____1____1____1____1____1____1
1____2____3____4____5____6____7____8____9____10___11
1____3____6____10___15___21___28___36___45___55___66
1____4____10___20___35___56___84___120__165__220__286
1____5____15___35___70___126__210__330__495__715__1001

Although I did the table differently. The number of paths at any square is the sum of the number of ways to get to the one above and to the left.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Andrew_S » Sun 04 Nov 2007, 18:19:13

I get 1001 with this C program:

$this->bbcode_second_pass_quote('', '/')* villageidiot1.c */

#include <stdio.h>
#include <stdlib.h>

int h, i, j, k;

int
main()
{
int num = 0;

for(h = 1;h <= 11;h++){
for(i = h;i <= 11;i++){
for(j = i;j <= 11;j++){
for(k = j;k <= 11;k++){
num += 1;
}
}
}
}
printf("%d", num);
return 0;
}


The first down step (variable h) is from column 1 to 11, the next down step (i) from h to 11, then j from i to 11, and finally k from j to 11. That delineates all the possible paths: 1001 of them.

I'd like to get an equation but too tired at the moment.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Andrew_S » Sun 04 Nov 2007, 18:22:56

$this->bbcode_second_pass_quote('dinopello', '')$this->bbcode_second_pass_quote('SteinarN', 'I')'m pretty sure the right answer is 1001. I havent found a formula to get the answer, but i made a table. In the right upper corner there is only one alternative route, hence the numper one. In the field to the left from the right upper corner you have to go down to field 4 to have another path. From there it is 4 different paths to the lover left. In the field one mor to the left there is 20 different paths to the end. And so forth.
286+220+165+120+84+56+35+20+10+4+1=1001


_____________________________________________________
I1001_I_____I_____I_____I____I____I____I____I____I____I__1_I
I_286_I_220_I_165_I_120_I_84_I_56_I_35_I_20_I_10_I__4_I____I
I__66_I__55_I__45_I__36_I_28_I_21_I_15_I_10_I__6_I__3_I____I
I__11_I__10_I___9_I___8_I__7_I__6_I__5_I__4_I__3_I__2_I____I
I___1_I___1_I___1_I___1_I__1_I__1_I__1_I__1_I__1_I__1_I____I


Exactly.

*____1____1____1____1____1____1____1____1____1____1
1____2____3____4____5____6____7____8____9____10___11
1____3____6____10___15___21___28___36___45___55___66
1____4____10___20___35___56___84___120__165__220__286
1____5____15___35___70___126__210__330__495__715__1001

Although I did the table differently. The number of paths at any square is the sum of the number of ways to get to the one above and to the left.


Both are very nice. I like the simplicity of the last one. :)
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby Bas » Sun 04 Nov 2007, 18:29:38

there's no equation; you have to use combinatoral mathematics for the easiest way to get to the answer:

14!/(10!*4!) = 1001

I also believe 1001 is the correct answer.
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Re: Math Problem -- Grid Possibilities -- (TOUGH)

Unread postby inculcated » Sun 04 Nov 2007, 18:32:52

Must be a trick question....
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