Re: Friday Puzzler -- Pinewood derby races

Larry Barrett
Here may be a way to reduce the races a little. Lets identify the first round races as A, B, C, D, and E, and the cars in each race as A1, A2, ... A5, etc.
Run the first 5x5 races and eliminate the slowest two from each race; ltes say for convenience that the slowest cars in each of the first round were cars 4 and 5 in each race. So after the first 5 races, 15 cars remain: A1, A2, A3, B1, B2, ... , E1, E2, E3. Again for convenience lets say that they finished in this same order: A1 won the first race, A2 finished 2nd, A3 finished 3rd, etc.

For the next race, select the fastest car from each of the first 5 races: A1, B1, ... E1. After this race, lets say that they finished in this order: C1, B1, A1, D1, and E1. So D1 and E1 are eliminated, and also D2, D3, E2, and E3 are eliminated since they were slower than D1 and E1 in the first round. Also, we can eliminate A2 and A3 since A1 finished in 3rd place in this race and A2 and A3 were slower in the first round, and we can eliminate B3 since we know that C1, B1, and B2 are faster.

So after the 6th race the remaining cars are C1, B1, A1, and C2, C3, and B2. B3.

This s as far as I can go for the time being.

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