5 Room House Puzzle

Someone showed me the 5 Room House Puzzle in the third grade. I worked on it a few hours every year until I was in graduate school. (Yes – a few hours every year!)

Have you worked on the 5 Rooms House Problem? http://mathfour.com/?p=9146 Only after 20 years, did I realize its complexity. And that it’s impossible.

There was no internet back then. Or at least none that I had access to. So I was unable to discover the futility of my endeavor.

But is working on the 5 Room House Puzzle futile?

Thinking and learning include two things: knowing what the problem is, and struggling to figure out the solution.

The benefit of working on the 5 Room House Puzzle is that you learn, in your gut, how to state the problem.

Various questions on the way to stating the problem are:

  • If I worked through this systematically, can I find the solution?
  • Is there a different way to look at this?
  • Is there some importance behind the five rooms?
  • If I change the number of the rooms or the layout of the house, does that make it easier?

The original problem is never stated correctly.

In many explanations of how to solve word problems, you’ll see the statement, “Rewrite the problem in your own words.”

That’s because the question, as it’s written, isn’t always what it seems.

And this is the case with the 5 Room House Puzzle. The solution isn’t the path through the doors. Nor is it the fact that it’s impossible.

The solution is the answers to:

Why doesn’t it work? What would make it work? Am I convinced that it’s impossible, or am I just trusting the Internet?

Assign the 5 Room House Puzzle to your kids!

I will occasionally assign the puzzle to a group of students. I usually offer them a reward of one dollar to each person who can solve it.

If I offered them $1 million, they would be suspicious.

Sometimes I look at it as¬†vengeance: “If I worked on this problem for 20 years, so should you.”

But mostly I know that if I ask the right questions, I’ll encourage thinking and learning.

How about you? Will you assign it?

Share your thoughts and experiences in the comments!



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6 Responses to 5 Room House Puzzle

  1. Ms Crowder,
    It may be of interest to you that this drawing (without spaces for the doors) was given as early as 1844 by T. Clausen as a different type of line puzzle. His challenge was to draw or retrace the original outline of the figure with the minimum number of restarts (pick up and move the pencil)
    I have not been able to find when it took up the “5 rooms” approach of crossing each wall.

    Also it was reported that Shongo children in the old Congo in Africa used to have contests drawing outlines like these and deciding which could and could not be a single path. Not sure how late this would have been, but probably early 20th century.
    Pat Ballew recently posted..On This Day in Math – March 5

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