Snarkbusters Inc. produces and deploys snark detectors, to be used on building f

Question

Snarkbusters Inc. produces and deploys snark detectors, to be used on building facades. These are very expensive devices. One of the company’s workers dropped a snark detector while working on the 16th floor of a building in Melbourne’s CBD, and the device broke when it hit the ground, in spite of having a reputation as indestructible. The company now wants to know how tough their snark detector really is. They have hired a consultant, Dr. Eva Luator, to determine the largest floor level from which a snark detector can be dropped without breaking. That is, they want the number n such that dropping a snark detector from level n is safe (it does not break), but dropping it from level n + 1 is unsafe (it will break). They call that number n the “safe limit”. They know that there is no problem when the device is dropped from ground level, that is, they know that 0 n < 16. Since there are 15 floor levels to test, Dr. Luator asks for a handful of snark detectors to use in the experiment. Once a snark detector is broken it cannot be used again in the test. But the company will not give her that many. They argue that one is enough, because Dr. Luator can just drop it from level 1, and then, if it did not break, drop it from level 2, and so on. That process will identify the safe limit. Dr. Luator protests: that could make the testing too time consuming (and expensive) because, in the worst case, she would need to perform 15 experiments (drops). As a compromise, it is decided that Dr. Luator can have two snark detectors to use in her testing. Eva Luator wants to make the most of the two snark detectors. She wants to minimise the number d of experiments (drops) that she needs to do, in the worst case, to determine the safe limit. What is that number d, and what is the testing strategy that achieves it?

Explanation / Answer

If there are two snarks.

A possible approach can be two consecutive levels can be tested together. If both the snarks break then the lower level will give the unsafe limit.If the
higher one breaks then the lower one will give the safe limit. So in such a strategy we will be needing 8 drops to test 16 floors. One important thing is
snarks must be marked or there should be a distinguishing feature so that when both fall , we can know which one(its floor number) has broken.

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