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Somewhere on a sphere - math puzzle
What is the mean distance between two randomly choosen points within a sphere of radius 1?
Quack medicine? - science puzzle
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According to homeopaths the effect of a homeopathic medicin is indicated by a dilution factor. Their theory is that if a substance is diluted more, the effect of it will increase. The dilution factor of a homeopathic medicin consists of a number and a character. An X or D indicates that the substance is diluted a number times 10. A C stands for a factor 100. As an example, 6 X indicates that the substance is diluted 10^6 = 1,000,000 times. Typical dilution factors of homeopathic medicins lie between 6 X and 30 X.
Suppose you bought a litre of homepathic medicin with a dilution factor of 30 X. Assume that water was used for the dilution proces, and that the molecules of the substance are about as big as the water molecules (smaller is almost impossible, since water is one of the smallest molecules). How many molecules of the substance can you find in your bottle. And how many litres would you need to buy to be sure that you will have at least one molecule of the substance? |
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Thunder and lightning - science puzzle
| Why does a flash of lightning take only an instant, while the corresponding thunder can last for a few seconds? You might have expected that that the sound is caused by the flash, and that the thunder should therefore be audible also for an instant. |
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