This challenge reminds me of two programs that I am pretty sure were on the discovery channel and are fairly indicative of the quality of science and rationality of much of the programming on that network.
In the first, a team wanted to test the viability of a giant bow that is found in DaVinci's notebooks described in much detail. They apparently had substantial funding from some unnamed benefactor and also had some unexplained inviolable deadline. The show was mostly about the travails of ordering the wood beams of the exactly right sort and fabricating the huge bow to DaVinci's specifications. This, of course, had to be accomplished in some remote area of Italy. When some key components of the bow didn't arrive on time, they severely modified the design to accommodate the materials they had. After many missteps, they finally completed the bow and celebrated their great success - a bit prematurely. When they tested the bow for the first time, drawing the bow string (actually, an inch thick cable) with much drama and tension in the faces of the onlookers...back, back, back...snap! The whole contraption broke apart.
Their profoundly metaphysical conclusion from this experiment: Because their bow, not built to DaVinci's specifications, did not work, they had shown that a bow that was built to those specifications would probably work!!!
The second show involved a test of whether the Greek soldiers secreted in the bowels of the Trojan horse (doesn't that elicit a wonderfully illicit image?) could really wait out the hours in their dark, cramped confine until it was time to exit the horse and destroy the city. Their first challenge was to build the horse since there is no record of what it might have looked like. In fact, most scholars of that period seriously doubt that there ever was such a plan or contraption - that it was a later elaboration of the story (remember that Homer wrote his account 400 years after the story). But they built the horse (in Turkey, of course, near the site of ancient Illium). Once built, they placed about a dozen men inside with a low light camera and a microphone so we could follow their response, with the intent of leaving them inside for about 16 hours.
Except these were not hardened Greek soldiers. They were just some local Turkish guys they found hanging around the construction site. After an hour or two, the "soldiers" complained about the still air and fumes in the under-ventilated interior. After four hours they complained of getting cramps from being jammed inside the horse. After six hours they started fighting amongst themselves and all discipline broke down. Finally, the exercise had to be stopped well short of the intended time.
Their conclusion: they had scientifically demonstrated that the Trojan horse story could have been true!
The point is that if some creationists were to take you up on your challenge and build an ark and try to stock it with two or 14 animals of every kind and try to maintain these animals for 300 days, they would scientifically prove the the ark story is not only possible, but is highly probable. Even if only one tenth of the animals actually fit in the ark, or if the carnivores ate all the herbivores, or if the elephants smashed the sides of the ark causing it to sink, or if most the animals and all the humans died of asphyxiation from the fetid gases from all the dung, or even if the ark just collapsed when the door was slammed shut, they would have proven the accuracy of the genesis account.
The human mind is an omnivore. It is quite capable of digesting the delicate logic of rational arguments. It is equally able to dine on raw, unadulterated bullshit.