Here is a fun problem to start this month off, in the diagram below, each "path" from top to bottom correctly spells that word MATCH. What is the total number of different paths in this diagram? Please post your answers and explain how you figured it out below. I will post the answer next week.
This brainteaser was developed by the Mathematical Olympiads for Elementary and Middle Schools.
is 4. Just counted them.
Think I'll have this paragraph in every post: Even mediocre web design would have a "log in" link go to a place to log in. The link should honestly say "click here to begin an unnecesarily tedious path to actually post anything." This site still has a link to "log in" that links to a different page that informs you that you haven't logged in. You have to search the page for the actual link to log in. Then when you do log in, it takes you to the home page so you have to navigate to your former position. I suppose making it take a long time to post is designed to ... ???
By counting the possible branches, I found 3 possibilities for each "M A" option giving me six options... wondering if there are any other paths.
Now, this assumes I *can't* go over to the third T from the first A, which is a cultural "knowledge" of how games are usually set up. If I could "skip" spaces then this would be more like regular probability & stats problems and I could plug in 2 x 3 x 2 and say "12 possibilities."
S Jones, I agree with your first paragraph strongly enough that I logged in to mention it. :) I'll save my rant about the high-security password requirements...
Also, isn't it interesting that we assume that rules from other games will transfer to new ones? I started playing this a while back: http://www.mathplayground.com/mobile_2048.html and it took me quite a while to realize that it wasn't like tetris--you can make the pieces go up as well as down or sideways...
I think that question about when to assume that old rules apply would be a great conversation to have in class. A lot of students come in assuming that this is going to be just like high school, and they are SHOCKED when I don't want to mark every single paper down in my (nonexistant) grade-book. Or, more insiduously, they assume that since nothing made sense in high school, nothing here will make sense either, so why review a problem if I guessed the right answer this time?
I am glad you chimed in - and I would love to hear more about your thoughts (rant) about high-security password requirements. We might share the same perspective :-) (send me an email offline - email@example.com). But I logged in to say that the agree with you and Sue about the the discussions that happen when developing strategies to solve these types of problems - when do we assume this or that? What information is needed? Do we know everything about what the problem is asking? We aren't only teaching math - we are teaching students to thing beyond the problem which for many is a new concept.
Thank you all for your participation this week. Here is a link to the NCTM Illuminations Brain Teaser problem with solution: http://illuminations.nctm.org/BrainTeasers.aspx?id=4755
I will post another problem soon.
Guess my answer was way short of the total number.
It's okay that your answer wasn't 100% - I appreciate your efforts. Plus, it is always good to hear how others "see" the problem. So thanks for posting how you arrived at your answer.