# Dividing nine children equally among five couples

Nine children are available for adoption and are to be divided equally between five couples; how many children are given to each couple?

This is a question from Foundations of Mathematics by Ian Stewart and David Tall.

The simple answer is that each couple gets one child, with four children left without adoptive parents. Obviously we can't divide up a child into fractions.

I don't think this is a combinatorics question, i.e. find the number of ways that nine children can be divided among five couples so that each couple gets at least one child.

Maybe there's a way to rotate the nine children (endlessly) among the five couples so that each couple gets to spend an equal amount of time with each child. If this is a viable solution, how might I go about approaching it?

Alternatively, we could play with the word "couple." What exactly is meant by a "couple"? We could three couples of two adults each and one "couple" of three adults (i.e. polygamists). The first three couples get two children each (3*2 = 6). The last "couple" gets three children (3 * 1 = 3).

Maybe I'm overthinking. If anyone has alternative theories, I'd love to hear them.

Edit: As @Ethan Bolker points out in his answer, the simplicity of this question is more obvious in context (i.e. the authors do not expect an answer). He found the original quote from the book and I am adding his screenshot below for clarity. When the authors wrote that "how can the mathematical formula be qualified", I interpreted it as a challenge to find a sophisticated answer.

• I think that this question is very ambiguous. In order to solve a problem, we first need a good understanding of what the problem is, so I suggest you refine your question and then we can begin to explore the mathematics. Mar 31 '17 at 17:54
• the problem here is that $9$ is not divisible by $5$, hence they cannot be "divided equally". Mar 31 '17 at 17:54
• @Isaac Browne: Thanks for your input! Ethan Bolker has correctly addressed the ambiguity and quoted the full question, showing that the authors do not expect an answer. Mar 31 '17 at 19:03