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The elephant and the boat

Timeless ingenuityLevel 2/5

One of the most elegant ways to weigh what cannot be put on a scale: replacing an impossible weight with another measurable one without losing accuracy.

A rajah wants to find out how much his elephant weighs, but he doesn't have a scale capable of supporting it. It does have the following:

  • a boat that perfectly supports the weight of the elephant,
  • a pier,
  • and as many 1 kilo stones as you need. How can you find out the weight of the elephant using only those things?
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Hints

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  1. The boat does not measure weight directly, but it can show when it is carrying the same weight as before.
  2. First use the elephant; then replace it with something else.
  3. Mark the level at which the boat sinks with the elephant inside, and then try to reproduce exactly that same level with stones.

Solution

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The elephant is placed in the boat and allowed to sink to its natural level. The corresponding waterline is then marked on the hull or next to the pier.

Then the elephant is taken out and 1 kilo stones are added until the boat sinks again to exactly the same mark. At that moment, the total weight of the stones is equal to the weight of the elephant.

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