## Thursday, January 30, 2014

### Don't Pay the Ferryman

I love story problems that look like they don't have enough information but they do.

The Futility Closet, an excellent source of puzzlers, had a beauty today. I wanted to dynamicize it to make a visual, and to allow for new numbers and a mechanism to provide for guess and check strategies. Here's the applet, which is also on GeoGebraTube.

What makes this solvable?

I have older sketches of two other problems, an escalator problem, via Bowman Dickson, and a burning candle problem, originally from NRICH.

Does the visualization add to the problems for you? Or does it not make a difference? Do these kind of problems engage you? I do worry about the frustration barrier with these, and am interested in how you might scaffold them.

The GeoGebra was fun. The most complicated piece was building a piecewise function that modeled the movement of the ferries. After the numbers are randomly generated, the sketch has the times for the ferries to cross, and then it's a point-to-point parameterization modified with graph transformations. It was fun to figure out as it took a lot of wee algebra bits to fit together.

The title is a nod to this Chris de Burgh song from the heyday of music videos.

#### 1 comment:

1. The fact that the only number in the problem is in minutes, but the requested answer is in miles, indicates that the problem is not mathematical. A closer look reveals that the "m" in "miles" is missing. Therefore, the answer is 5, which is the number of islands ("iles"), indicated as dots on the "o" in "GeoGebra".