In the village of "Rain," no rain had fallen for three years. The wells had dried up one after another, except for one ancient well underground, said to have been hidden by the ancestors behind one of three doors in a cave on the edge of the village.

The village elder stood before everyone and said, "There are three doors. Behind one lies the well of water. Behind the other two lies a dry, deadly ravine — whoever enters does not return. The ancestors wrote a sentence on each door, and left us a single rule: exactly one of the three sentences is true, and the other two are false."

Rima, a girl of twelve, stood among the crowd holding an empty bucket, listening in silence. Her grandmother used to say Rima thought like an old woman. Her father used to say she asked too many questions.

The elder read the sentences written on the doors:

On the first door: "The water is behind this door."

On the second door: "The water is not behind this door."

On the third door: "The water is not behind the first door."

Then he said, "We have one day. Whoever enters the wrong door does not return. I won't send anyone until we know."

The men began to argue. One said, "The first door says the water is behind it. It must be the right one, since it's the first door." Another said, "No, it's the last one — the ancestors always hide the most important thing at the end." A third said, "Let's draw lots." Voices rose, and the men nearly came to blows.

Rima sat on a rock in a corner of the cave and took out a small piece of charcoal and a flat shard of pottery from her pocket. She wrote down the three sentences, then said to herself quietly:

"The rule is that exactly one sentence is true. Not two, not three. I'll test every possibility."

And she began to write.

"First: suppose the water is behind the first door. Then the first sentence is true. And the second sentence says the water isn't behind the second door — which is also true, since the water is behind the first. So that's two true sentences. That breaks the rule. The water isn't behind the first door."

She crossed out the first possibility.

"Second: suppose the water is behind the third door. The first sentence is false, since the water isn't behind the first door. The second sentence is true, since the water isn't behind the second door. And the third sentence is true, since the water indeed isn't behind the first door. So that's two true sentences again. That also breaks the rule. The water isn't behind the third door."

She crossed out the second possibility.

Rima looked at what remained. Her fingers were trembling slightly.

"Third: suppose the water is behind the second door. The first sentence is false, since the water isn't behind the first door. The second sentence is false, since it claims the water isn't behind the second door, when it is. And the third sentence is true, since the water really isn't behind the first door. So that's exactly one true sentence and two false ones. That matches the rule perfectly."

Rima stood up and raised her voice above the men's noise: "The water is behind the second door!"

Everyone turned to look at her. The elder asked, "How did you know, my daughter?"

She showed him the pottery shard. He said, "We'll test it. But not with a person."

They tied a long rope to a bucket and lowered it through the opening of the second door, and after a moment they heard a sound none of them had heard in three years: water striking metal. They pulled the bucket back up, and it was full of clear, cold water.

The people cried out with joy. The men lifted Rima onto their shoulders. And her grandmother's eyes shone as she said, "I told you — that's the mind of an old woman."

That night, before she slept, her mother asked how she hadn't been afraid to go against all the men. Rima said, "I didn't go against them. I tried every possibility in order, and whoever tries every possibility doesn't need courage. All they need is patience."

The Solution in Brief

The rule: exactly one sentence is true.

• If the water were behind the first door: the first and second sentences would both be true. Rejected.

• If it were behind the third door: the second and third sentences would both be true. Rejected.

• If it were behind the second door: only the third sentence would be true. Accepted.

So the water is behind the second door.