Not a whole lot of action on last week’s, but it was admittedly a little time intensive.

This week’s problem:

A basketball court is made up of square parquet tiles, all the same size, laid side by side to form a rectangle 105 tiles wide and 135 tiles long. If a straight line is drawn diagonally from one corner of the floor to the opposite corner, how many tiles will the diagonal intersect?

Part II: Generalize.

See you in the comments or on twitter!

### Like this:

Like Loading...

*Related*

I’m interested, do you let all your students “open source” their math homework or do you make them do it on their own?

Depends on the nature of the assignments – these weekly problems were assigned specifically to us with the intent being that they be collaboratively answered – with other members in our cohort, with our students, with colleagues, or as I’m doing with my online network.

If the assignments had the intent of “practicing” a specific skill, this approach would be less helpful to me unless I had a specific questions I needed answered. In the context of collaborative problem solving, it’s been a great experience so far to compare all the different ways of approaching the problem.

And, the even primes question is far from finished – we are now *attempting* to put together a class solution for it.

Originally I was going to start with a 9×7 rectangle and scale up looking for a pattern. But I think somewhere in here there’s a really beautiful way of doing this that I can’t see yet. I *really* want the solution to include two things:

1. The symmetry of the two triangles that are created when it’s cut diagonally.

2. The minimum number of “uncut” squares in a triangle.

In my head I picture this as a logic or geometric solution.

Looks like we have the same instinct as that was where I planned on starting. I’ll get back to this tomorrow afternoon during my breaks from the hardwood install…

(Also, I really need to update the even primes post as I go to school with ppl WAY smarter than me and it’s not over yet… I think you’ll enjoy what’s going on.)