I'm trying to solve a riddle but not sure how to go about it. Here goes. There are ten groups of identical objects. Each group has one more then the last. So in other words the first group has one object, the second group has two objects, and so on. Someone comes along and combines all the groups into two piles. Pile "A" has 42 and pile "B" has 13. Which groups were combined to create pile "A" and which groups were combined to create pile "B". A possible solution to this is as follows.
"A" = [2,3,4,6,8,9,10]
"B" = [1,5,7]
I have three main questions relating to this.
Are there other possible solutions to this question? I hope not. :)
It seems like there should be a way to do this algebraically. Is there?
This question is the most important. Is there a way to solve this same problem on a larger scale? let's say you were given the same problem but there were 1,000 or even 1,000,000 groups. I'm looking for a way to solve this larger scale issue with only one solution. If that's not possible to do as is than it's OK to add a variable before the piles get combined. I'm not sure if that would even help but it's within the constraints of this question if needed.
I'm also not really sure what tags to apply. So if there is a tag that should or should not be tagged here please let me know.