Area & Geometry Reasoning
The General's Horse: A Famous Chinese Shortest-Path Puzzle
A general rides from camp to the river, lets his horse drink, then rides to his tent.
1:29
Step by step
- Camp → river → tentA general rides from his camp to the river, then on to his tent.
- Where should he stop?His horse must drink at the river. Where should he stop to make the whole trip as short as possible?
- 7.3 … 6.7 … where's the best spot?Let's try a few spots. Here, the trip is seven point three. Here, it's six point seven. So where's the best spot?
- Fold along the river: the tent lands on B′Here's the trick. Fold the picture along the river, like a mirror. The tent lands on the other side. Call this new point B prime.
- Any spot P: PB = PB′Now watch. From any spot on the river, the tent and its mirror image are exactly the same distance away.
- Flip it down: the trip to B′ is just as longSo flip the last part of the path down. The trip to B prime is exactly as long as the trip to the tent.
- Shortest from A to B′: a straight lineNow it's easy. The shortest way from A to B prime is a straight line. Where it crosses the river is the best spot!
- Flip back: the shortest routeFlip it back up, and there's the general's shortest route. Stop anywhere else, and the path bends, so it's longer.
- Reflect → Connect → CrossSo remember: reflect, connect, and cross.
Your turn
Your turn. The camp is three from the river. The tent is five from the river. And they're six apart along the river. What's the shortest trip?
Show the answer
Fold the tent across the river. Now the straight line is the long side of a right triangle, with sides six and eight. Six squared plus eight squared is one hundred, which is ten squared. So the shortest trip is ten!
Keep going
There are more short lessons on this topic, each with a full write-up. A free 15-question fractions check-up is coming soon.
