Okay, I hope the mods are all right with this homework request, for several reasons:

- The professor didn’t care whether I got the right answer to the problem or not.
- The professor hasn’t figured out the answer to the puzzle herself.
- The class is over and I aced it.
- With my help, the professor came closer to the answer than she’d gotten in sporadic work over the past several years.

This is a math puzzle, one of two that a math-for-children prof gave us to solve as a way of figuring out how we approach math problems for which we don’t have a ready-to-use algorithm (her idea is that we should understand our own thinking so that we can better help kids develop logical thinking about math). The problem is as follows (paraphrased):

There are nine people:

Bill, Mary, Tom, Eliza, Hank, Susan, Ned, Sarah, and Jake.

They’re subdivided into three families, with a mom, a dad, and a grandkid in each family. Last names are Jones, Brown, and Smith. One parent from each family is related to Grampa Smith: one’s a daughter, one’s a son, one’s a stepson.

Grampa Smith, a loathsome slaver, dies in the nineteenth century. He wills his money to these three families in a complicated fashion, with the following rules:

- A set number
*n*describes the difference in inheritance between each member of each of the three families. The husband in each family receives n dollars more than his wife, and the wife receives n dollars more than the kid. - The inheritance is parceled out exclusively in 1-dollar bills.
- Each heir receives a packet of envelopes with money in them; the money in each envelope equals the number of envelopes in that heir’s packet.
- The sum of Mary and Sarah’s inheritances equals the sum of Tom and Bill’s inheritances.
- The sum of Ned, Bill, and Mary’s inheritances is $299 more than Hank’s inheritance.
- The sum of the Jones family’s inheritance is “altogether over one third more than” the Browns’s inheritance.

The quesiton is, what are the last names of the family members, and how much does each receive?

I’ll describe where I’ve gotten with the puzzle later.

Daniel