I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

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Tag Archives: puzzles

Puzzles and Riddles that Improve Math Ability

This is Day 11 of 31 Days of Math Learning Success. Follow all the days here and check out others that are writing for 31 days here.
Puzzles and Riddles improve math and logic skills. Here's a list of good ones to try!

“The solution often turns out more beautiful than the puzzle.”
~Richard Dawkins

“Did you always like math?” I was asked once.

It was a strange question, because I’ve never really liked math.

After pondering it, I realized that I’ve done well in math because I’ve always liked puzzles!

Puzzles & Riddles Instead of Math

Puzzles and riddles get your thinking juices flowing. And math is all about thinking.

To improve your math skills, start doing more puzzles and riddles.

Note: “puzzles” are not limited to jigsaw puzzles. In fact, I don’t even think about that kind when I use the word puzzle. Although I’m sure they have a benefit on thinking and processing too.

Here is a list of some of my favorite puzzles and riddles, along with some great places to find them:

Some puzzle/riddle collections:

You can even invent your own puzzle or create a maze!

Have fun!


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2 Responses to Probability Tree Diagrams as Puzzles!

    • Yes, Alice, there are a few.

      1. I’m crazy busy with lots of other things.
      2. This is a minor error that only one person in 2.5 years has noticed.
      3. The important content of the piece is error-free.
      4. I have a list of things to do on the blog that has about 130 things on it.
      5. It’s nice to let others discover the error too.

      All things taken together, it’s just not even on the list to get fixed.

      However, I appreciate you commenting about it so that others will know that when they find the error, they aren’t crazy. :)

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15 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.

  2. My wife gave this to me and said a lawyer she works with has been trying it since 7th grade with no success…I, naturally, had to either do it or prove that is couldn’t be done.

    Can’t be done.

    The three bigger blocks have 5 sides, while the two smaller ones have 4.
    This means 5 and 4 lines must be involved in those blocks to satisfy the goal.
    The two smaller could either have lines go in, out, in, out (ioio) or oioi.
    That works because no line is trapped inside or outside.
    A five sided box, however, has to go either ioioi or oioio, which can not be sustained.

    The total amount of lines has to be uneven:
    2, 4 sides boxes plus 3, 5 sides boxes
    (2)ioio + ioioi + (2)oioio
    (2)(2i2o) + 3i2o + (2)(3i2o)
    4i4o + 3i2o + 6i4o

    The ins and out don’t match so a line will always be separated from the goal.

    Try with any number of 4 sides blocks and it is always possible, as it is with any even number of 5 bordered blocks.

    The only way to win is to have a single line go through a joint (high would count as crossing 3 lines at the same time but that is, apparently, not allowed.

  3. Actually, I don’t think it’s doable with multiple 5 sides boxes because it eventually/immediately excludes the lines from each other.

    • Indeed, JustMyke. It is impossible. Alas, a more formal proof of this exists. I believe it’s a Graph Theory thing, but I haven’t looked at it in years.

      Thanks for stopping by!

  4. This was given to us in 6th grade in our Apex group…..the only solution we ever came to was this.
    The rules state one Continuous line that does not cross through the same wall twice…..so we drew a small 5 block puzzle (5 room house) and one continous line going from the top right corner to the bottom left or vice versa….the catch the line was ultra thick so that it covered the entire surface

  5. If you’ve had a course in Graph theory, this isn’t a difficult question anymore. The problem can be seen as a graph of 6 vertices (rooms A, B, C, D and E, and the area F outside the rooms). Looking at the drawing, it is clear that the valency of vertex A is 5, which is an odd number. Then it’s immediately clear that this graph can’t be an Euler graph, so there doesn’t exist a circuit that passes all edges (the doors between the rooms).

    • Great point, Sander. Alas, I was in the third grade when I started on the problem. And it wasn’t until my graduate course in Graph Theory (my only one) that I learned this. It was a long time between 8 years old and grad school. #sigh

      Thanks for stopping by! :)

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2 Responses to A Halloween Puzzle: Rubik's Cube

  1. I love her costume!! So cute! There is 1 green and 9 orange squares missing. It is not possible to twist the Rubik’s cube into this combination. Each center cube on each side does not move (it is fixed) so the blue in the center and the back is not possible.

    • Lindsay, you’re brilliant!

      I was thinking that the bonus would be super hard. You looked right for the simple thing to start – are there unique middle squares?

      (Reading your answer and seeing your site makes me wonder if there’s a message in the binary code on the header…)

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7 Responses to Riddle: What are the ages of the kids?

  1. I’m going to give this to my logical daughter who says she doesn’t like math but always is able to solve these kinds of questions.

  2. I have to admit I haven’t really sat down to tackle this yet, but…I’m feeling a bit stupid that I don’t see how the last bit of information has any bearing on the numbers. How does where the children are tell us anything about how old they are? Numerically, it doesn’t say anything except that they aren’t ALL the same age. But that wasn’t a possibility in the first place, was it?

  3. I think my daughter and I solved it. But if so, I think the riddle is imprecise. Will wait to see if hubby (the math wiz in our house) arrives at the same conclusion by the same reasoning.

    • Good point, Rachel. Although I do think the intent was “older” means “a different integral number of years.”

      But indeed, it is still a bit imprecise. :)

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