blackhole01
New member
- Joined
- Nov 22, 2018
- Messages
- 2
Hi everyone
I'm new here and don't speak English very well. A couple days ago my math teacher gave us (my class) a math problem which we have to solve before Saturday, but we can use anyone to solve it except our teacher or other teachers at school. It's a bit about probability so my class and I aren't really good at solving since we're going to see it after winter break. I hope you guys can help us solve it! The problem goes as follows:
During WWI the Germans have created a minefield with 6x10 squared cells. They have only 16 mines and are placed randomly in the cells like this example
A scientist of the English army has luckily created a mine detector. This mine detector can detect the radiation of the 8 closest cells (or less if you are close to the edge.) But when there are more than 6 mines near the mine detector (7 or 8), it will explode and become useless. The scientist tries to calculate the average of how much cells (without a mine) in the mine field can be with more than 6 neighboring mines. These cells are called dangerous cells.
If you know that the mines are placed randomly, how many dangerous cells can you expect on average? Notice there are 2 different types of dangerous cells as shown at the example above.
a) Give for each type of dangerous cells the average number.
b) What happens if you double the width and the amount of mines?
Now we have given a try at this problem. We came to conclusion that you have 60!/44! different setups, but that's all that we can find. I really hope that someone can help us find a solution to this problem. It would really help us a lot. Thank you!
I'm new here and don't speak English very well. A couple days ago my math teacher gave us (my class) a math problem which we have to solve before Saturday, but we can use anyone to solve it except our teacher or other teachers at school. It's a bit about probability so my class and I aren't really good at solving since we're going to see it after winter break. I hope you guys can help us solve it! The problem goes as follows:
During WWI the Germans have created a minefield with 6x10 squared cells. They have only 16 mines and are placed randomly in the cells like this example
A scientist of the English army has luckily created a mine detector. This mine detector can detect the radiation of the 8 closest cells (or less if you are close to the edge.) But when there are more than 6 mines near the mine detector (7 or 8), it will explode and become useless. The scientist tries to calculate the average of how much cells (without a mine) in the mine field can be with more than 6 neighboring mines. These cells are called dangerous cells.
If you know that the mines are placed randomly, how many dangerous cells can you expect on average? Notice there are 2 different types of dangerous cells as shown at the example above.
a) Give for each type of dangerous cells the average number.
b) What happens if you double the width and the amount of mines?
Now we have given a try at this problem. We came to conclusion that you have 60!/44! different setups, but that's all that we can find. I really hope that someone can help us find a solution to this problem. It would really help us a lot. Thank you!
