Puzzles/How do you ... ?/The Burning Island/Solution

The man picks up a piece of wood and lights it from the fire on the west end of the island. He then carries it over to set fire to the middle of the island. Fortunately, the wind is hurricane strength, so the fire from the middle only burns the east side of the island.

The man then goes to the east side of the island, where the fire from the west side can't spread, because the east side has already burned down.

The man survives the fire, but dies of starvation, with all the food in the forest burnt.

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• Comments

1. The puzzle, as stated, does not assert that the entire island is covered by the forest, but the solution is trivial unless it is.
2. In a real fire, the smoke being blown eastward across the island would be as much of a danger to the man as the flames. (He must have had a source of fresh water on the island to survive... he could dip his shirt in that to use as a gas mask. He should also lie flat on the ground to try to stay below the smoke.)
3. The puzzle does not state anything about the flatness of the island. The presence of hills or canyons would affect the path the fire would take, possibly offering areas of safety due to the fire making its own fire break (a fire break being essentially the solution described above).
4. The fire set in the middle of the island would not burn the entire east side of the island, but only a triangular area extending eastward from the point the fire was set. The shape of the triangle would be determined by the balance between the tendency of the fire to burn outward in a circle from where it was started and the force of the wind. This being the case, and with the assertion of hurricane-force winds, the far end of the triangle, where the man would have to stand, might be too narrow to shield him from the heat and smoke.
5. Nothing in the puzzle asserts the shape of the island. The entire surface of the island burns only if the island perimeter is convex. If there are concave areas, a peninsula is formed, and the tip of the peninsula would be unscathed. The shape and size of the peninsula would be relevant, per the reasoning above about fire cutting a triangular shape. This solution has the added advantage that the tip of the peninsula would be free of smoke.
   1. If the island was a circle, which is a convex shape, and the fire burnt in a triangle, not all could burn. If the island was shaped like the concave Greek letter Λ (or the roman letter V) and the fire started at the tip, the whole island could burn. Currently, the problem states the whole island would burn without intervention, anyway.
6. When one considers that one does not typically find trees on a beach, the man could just make his way to the west beach. The fire and smoke would both travel away from him.

• um... if the island is circled by cliffs how is he supposed to get to the beach?

1. And if cliffs surround the island and he can't get back on, the most obvious question is: how did he get on in the first place?
   • Clearly he crash landed
2. Perhaps the man survives the fire by entering the luxurious fire-retardent home, complete with cable television and beer.
3. The puzzle doesn't state that the man would die on impact by jumping off the cliff. He could jump off the island and survive the fire. Most likely he would die of starvation or dehydration, just as he would on the burned out island as stated in the current solution.

• The man can dig a hole in the ground deep enough to withstand the fire for a few minutes which time would be enough for the fire to recede from his location.
• The man can cut part of the wood and therefore stop it from burning the whole island.