It’s back to school time in America, and students all over the country are starting new schools – and finding the best routes to ride home on their bikes. Well, assuming they ride straight home!

Here’s a math game to try.

How many routes can this student find to bike home, following the one-way streets?

We posted the puzzle on our Facebook page earlier this week and the comments were really interesting. Xuhui Li noted the similarity to the Jia Xian Triangle, and Debbie S said it reminded her of Taxi Cab Geometry – here’s a good list of Taxi Cab Geometry resource links from the Teaching Math Blog.

Kristine J commented that adding boxes (eg, 3×3, 3×4) and coming up with a pattern and mathematical formula for finding the number of routes would make it more interesting – adding that this type of puzzle is really helpful in getting kids to think algebraically.

The solution? The general consensus of those who commented on Facebook was that there are ten routes. That’s what we came up with as well, and here’s our screencast showing how we arrived at the solution:

UPDATE AUGUST 29, 2012 – we wanted to share Xuhui Li’s video response: