# Brain Teaser - July 1

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.

Have Fun!

Brooke Istas
istasb@cowley.edu

This brainteaser was developed by the Mathematical Olympiads for Elementary and Middle Schools.

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?