Marketing Math

C joined us in the car today so I put her on the spot and asked her to share something with us. She has been preparing an after-school program for kids who want to participate in math competitions. Yesterday she went to all the 6th grade classrooms in our kids' school to tell the kids about it. She gave the kids a problem as an example and asked those who would come to the first session to try to solve it. Afterwards one of the math teachers approached her and told her the problem was too hard and the kids would be discouraged. So C is worried about it. P thought it was good that it was challenging because that way it would attract the kids who took math seriously and were good at it. A said the problem with that approach is that some kids might turn out to be good with a bit of training and practice but would not get to that if they were discouraged with the first problem. I said the good thing about the specific problem she gave them is that a) it was a fun one, and b) kids wouldn't know if they got it right or wrong until C explained the answer. Furthermore, it is easy to take a stab at this problem, so that even if most kids got it wrong, I doubt they would get discouraged. We also discussed that she could have given them several problems (some easy some hard) to cater to all levels - and to quickly find out the level of the kids.

I mentioned to the boys that companies often face a similar challenge: in such areas as dieting, exercising, language training, gardening, etc., companies often start with easy steps to get customers hooked, and only move to harder more meaningful challenges after the customer is committed. Of course, some companies never go beyond the easy stuff, thus keeping their customers "happy" even if the results remain elusive...

What is the problem C gave the 6th graders? If an ant is standing on one of the corners of a cube, what is the shortest route it should take to walk to the opposite corner?