Chris Kulczycki wrote a book called "the canoe shop." In it, he describes how to build (and he includes plans) for three different canoes. The canoes are made of plywood panels, but I bet you could use cardboard instead. I think each canoe uses 10 panels to make the curves from one gunwhale to another and from one end of the boat to another. That means each individual panel only has to bend and twist a slight amount to achieve this overall shape. I bet cardboard could do this without kinking. I know you can stack many layers of cardboard to make a sturdy beam. You could do this at the gunwhales to beef things up. There are three designs in this book, a 12 foot, a 14 foot, and a 16 foot. I bet any of them would be fast enough to win the race. If you stagger your joints like a brick wall, the different panels should all help to reinforce one another, and the boat should be strong enough to finish the race.

The boats are intended to be built with epoxy to glue things together, but I bet tape would work fine for your event. You aren't going to be running any rapids or going out to sea in this thing, right?

I think you can also buy nice, full sized plans from www.clcboats.com, but buying the book would be a lot cheaper.

You can read 27 of the pages of the book for free at amazon.com. You may want to take a look at it there for ideas.