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.

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".

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