Open ended problem: Tables for a party


How many tables and how many chairs?



2 thoughts on “Open ended problem: Tables for a party

  1. I’m pretty sure that it is impossible. Here is my proof. Set aside one table that has x seats. So, all the other tables can hold 100-x people all together. Then, if 100-x people arrive and then just 1 more, the 1 more person is doomed to sit in the last table.

    • Yeah, it is impossible, but children don’t know that before they start working on the problem. I’m absolutely fine with students working on problems which are impossible to find an exact solution for, particularly if they can “prove” in some way why it doesn’t work. Also, it may be that students can find solutions which almost work. Not every problem needs to have a solution to be a source of rich mathematical thinking. Look at the Konisberg bridge problem for example, which led Euler to developing graph theory to prove that it was impossible to solve.

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