♟️ Strategy ★★★★☆ +22 points #7

Twenty-Five Horses

📜

This one has been revealed The solution is at the bottom of the page. Try it yourself first — an archive puzzle still counts, for half the points.

There are 25 horses. Some are faster than others, and a given horse always runs at the same speed — no ties, no off days.

The track has five lanes, so you can race five horses at a time. You have no stopwatch: a race tells you the order the five finished in, and nothing more. You can never compare times across two different races.

One race = the finishing order of five horses. No times.

You must identify the fastest three horses, in order.

🏁Racing all 25 in five heats and then racing the five winners gives you the champion, but not the correct second and third. Find out why, and fix it.

Answer to type: the smallest number of races that always identifies the top three.

💡 I want a nudge

After the heats and the race of winners, ask which horses are still possible candidates for second and third. There are fewer than you think — and exactly five of them.

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🔓 The solution

Answer: 7

Races 1-5: split the 25 horses into five groups and race each group. Now you know the order inside each group of five.
Race 6: race the five group winners. Call them A1, B1, C1, D1, E1 in the order they finish. A1 is the fastest horse overall — it beat everyone in its own group and every other group winner.
Now throw away everything that cannot possibly be second or third. D1 and E1 lost to three winners, so at least three horses are faster: they and their whole groups are out. C1 lost to two, so C1 is still possible but nothing behind it is. From group B only B1 and B2 survive; from group A, A2 and A3.
That leaves exactly five candidates: A2, A3, B1, B2, C1. Convenient — five is one race.
Race 7: race those five. The first two home are the second- and third-fastest horses overall. Seven races.

The trick: the work is not in the racing, it is in the eliminating. Each result rules out a whole block of horses at once, and the puzzle is really the question "who is still possible?" asked after every race. That habit — track the candidates, not the winners — is how tournaments, sorting algorithms and search problems are all analysed.

Previous puzzle: The Fork in the Road