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Let’s assume, you are in a rush and you need a random number: What is the best way to produce a high-quality, uniformly distributed random integer number between 0 and 9, ideally using only mental math or, less ideally, tools that are commonly available (except for computers, calculators, smartphones and books, of course).

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Is this common? random.org/integers –  Amzoti Jan 18 at 2:06
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Look at a digital clock and use the ones digit of the minute? –  Brad Jan 18 at 2:06
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How fast are you with scissors and glue? :-D –  J. W. Perry Jan 18 at 2:40
    
This is more pencil-and-paper rather than mental, but: en.wikipedia.org/wiki/Middle-square_method –  vadim123 Jan 18 at 2:58
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1 Answer

up vote 3 down vote accepted

Toss a fair coin four times. Put a 1 if the toss is a head and a 0 otherwise. Make the four tosses into a string of 0s and 1s of length 4. For example you might get 0110. Convert this binary number to decimal; in the example you got 6. Toss it out and try again if the number is > 9.

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For repeated tries, you can increase the efficiency by throwing 10 coins to produce 3 digits (try again if the number is in the (1000-1023 range) –  leonbloy Jan 18 at 3:48
    
C'est vrai; I was shooting for absolute minimality. –  ncmathsadist Jan 18 at 23:37
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