This "task" is supposed to show the problems with dividing by zero. However, how does one resolve this?
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When we are talking about dividing between 0 people, we're dealing with division by 0.
Logic says, given any empty set S, ∀x P(x) is always true. In other words, the answer is true for all elements belonging to the universe of discourse. This contradicts with the uniqueness property of a binary operation over real numbers. Hence, the answer is undefined.
On an informal note, it doesn't make a lot of sense when someone wants to divide 10 bucks between nobody. You need a non-zero number to start with and hence, division by zero is undefined.
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Everyone here immediately starts talking about dividing by zero, but we should first note that the question is not about dividing by zero, but about distributing cookies evenly among zero people.
The most important thing that we have to clarify here is the definition of "divide evenly".
Case 1: "Divide evenly" means that every person gets the same amount of cookies.
In that case, we could just give each one of the zero people exactly $17$ cookies and we're done. No two people have different amounts of cookies.
A correct answer, therefore, is "$17$ cookies".
However, this definition of "divide evenly" implies that cookies may be left over. According to it, we could divide $10$ cookies evenly over two people by giving each person $3$ cookies and leaving $4$ cookies over. This definition may not be the one we intended.
Case 2: "Divide evenly" means that every person gets the same amount of cookies, and there are no cookies left over.
In that case, we clearly can't divide $10$ cookies over $0$ people, since there are always $10$ cookies left over.
Now the premise of the question, "One distributes cookies evenly between $10$ people", is a contradiction.
A contradiction implies anything, especially that "$17$ cookies" is a correct answer.
Conclusion: "$17$ cookies" is a correct answer, no matter how we define "divide evenly".
I think there is not a good answer for this question, since it is a real live question. You can try to model it into a term or a formular that might be solved, but the answer depends on your model.
For example, you could just go for $\lim_{t \rightarrow 0} \frac{10}{t}$ and get the answer $\infty$, but you also could ask for the multiplicative inverse of $0$ in the $\mathbb{R}$ (to put it into $10 \cdot 0^{-1}$) and get "There is no solution for that.".