I'm currently a student doing A-Level further maths, however this problem has nothing to do with schoolwork. I am working with a friend to create a game and we were just interested in this solution. I've never come across a problem like this before and I'm not even sure how to begin to go about it.
You must choose one number from each column therefore totalling 6 numbers. How many combinations are there so that the sum of the numbers is less than or equal to 100?
So if I disregard the conditions, there would be a total of 66 permutations equaling 46656.
The highest sum possible is 165 whereas the lowest would be 0.
I could go about this the long way (by finding all of the combinations equalling greater or equal to 100 and then calculating number of permutations) but I feel that it would be inaccurate and I could be there forever. I'm not sure if there is a quicker and more accurate way to go about it?
| A | B | C | D | E | F |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 20 | 20 | 5 | 5 | 30 |
| 15 | 25 | 15 | 5 | 5 | 20 |
| 10 | 15 | 20 | 10 | 15 | 15 |
| 10 | 30 | 25 | 10 | 25 | 20 |
| 15 | 40 | 30 | 15 | 35 | 20 |
You must choose one number from each column therefore totalling 6 numbers. How many combinations are there so that the sum of the numbers is less than or equal to 100?
So if I disregard the conditions, there would be a total of 66 permutations equaling 46656.
The highest sum possible is 165 whereas the lowest would be 0.
I could go about this the long way (by finding all of the combinations equalling greater or equal to 100 and then calculating number of permutations) but I feel that it would be inaccurate and I could be there forever. I'm not sure if there is a quicker and more accurate way to go about it?