Solution: Horses, Horses
Your job, and possibly your neck, depended on finding the smallest number of races by which you could identify the top three horses.
This is the solution to last week's puzzle. If you haven't read the puzzle, start there.
Last week, you were tasked by your employer, Johnny "Mud Dauber" Daubins, to discover, with the utmost efficiency, the fastest three horses in his stable of twenty-five, given that only five horses could race at once, and you weren't allowed to record the track times. Your job, and possibly your neck, depended on finding the smallest number of races by which you could identify the top three horses.
If your answer was seven races, congratulations! Your place in the organization (and among the living) is secure. If not, here's a strategy that could have saved you.
Divide the horses into groups of five, and race them in five heats, so each horse runs once. This puts five races in the books, and gives you a winner for each. Those winners might be, for example:
Heat 1: Grin Tin Tin
Heat 2: Hi Ho Silver
Heat 3: Nickel Plate Road
Heat 4: Gold Coats
Heat 5: Bronzon Pinchot
Next, race those five winners against each other. (That's race #6) In our example, by pure chance, the finishing order is Gold Coats, Hi Ho Silver, Bronzon Pinchot, Nickel Plate Road, and Grin Tin Tin.
With that done, you can eliminate any horse who's slower than three others. (You can't be in the top three, if three other horses are faster than you.) Nickel Plate Road and Grin Tin Tin are scratched off the list, along with all the horses they outran in their respective heats.
You can also eliminate the four losing horses from Bronzon Pinchot's first race, since they're all slower than Bronzon, and he's slower than Hi Ho Silver and Gold Coats. The bottom three finishers from Hi Ho's heat are out of the running, too. Only Hi Ho Silver and Silver Belles (the second-place finisher from that heat) stay on as possible candidates for the overall top three. From the Gold group, the bottom two horses are out, while three remain: Gold Coats, Golden Slumbers, and Traipsey Gold.
That leaves six horses with a hopeful claim to the top trio: Gold Coats, Golden Slumbers, Traipsey Gold, Hi Ho Silver, Silver Belles, and Bronzon Pinchot. At first glance you might think you'll need split them up, but Gold Coats doesn't need to race again—she's already won her spot as the fastest overall.
Your seventh and final race will feature Golden Slumbers, Traipsey Gold, Hi Ho Silver, Silver Belles, and Bronzon Pinchot competing for the second and third positions overall.
(Sadly, Hi Ho Silver collapses in the seventh race. Listed on the board, inadvertently, as HI HO Silver, he breaks down into H2O and silver iodide.)
Puzzle Source: Presh Talwalkar, Mind Your Decisions.
