R Hansen says: >Setting the limit to 7 would certainly put this into the "trick question" category, like you see people pull on each other at bars.
R Hansen says: >Given the constraint of "7" races, which, along with every other pertinent condition, was left out of the original problem,
I wouldn't call it a constraint, but its natural in this context to look for the least number of races needed. As far as some of the other "pertinent condition", I noticed you failed to mention some of them.
1. No ties. 2. Two racers who race each other more than once end up in the same relative order. I thinks that's the intended condition that makes this a mathematical problem. Notice than in race#7 you have the second and third place finishers of race#6 going against each other again. One could institute a rule that race#7 is the official decider but that's not very mathematical.