there are 8 doors behind each door is a number each number is less than 20 no 2 numbers are the same they add up to 93 what are the numbers
You probably noticed that there are many possible answers.
One answer would be to take the numbers starting from 19 until they add up to more than 93, then replace it by a smaller number.
For example, start with
sum(19,18,17,16,15,5,2,1)=93
After that, you can change 2 and 5 for 3 and 4 to give:
sum(19,18,17,16,15,4,3,1)=93
Then 15 and 4 for 14 and 5,....
sum(19,18,17,16,14,5,3,1)=93
sum(19,18,17,16,13,6,3,1)=93
sum(19,18,17,16,12,7,3,1)=93
sum(19,18,17,16,11,8,3,1)=93
sum(19,18,17,16,10,9,3,1)=93
After that, you can repeat with 16 and 10.....
I have not counted the number of possible solutions with unique numbers (i.e. no two numbers are equal). But the number should not exceed C(19,8)=75582 answers.