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Comment by hueving | Hacker News Reader

>Easily solved by taking the last digit modulo the number of children, but I guess that might be difficult while driving.

Well it's not fair. Take 4 children for example. random 0 to 9 mod 4 does not have an even distribution over 0-4.

It's also more difficult to explain to children.

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> random 0 to 9 mod 4 does not have an even distribution over 0-4.

That's true, but only because 4 never appears in the result. The possible results for modulo 4 are 0 - 3.

The first child is numbered zero. Shall I explain it in more detail?

     n  n % 4
    -----------  	
     0  0
     1  1
     2  2
     3  3
     4  0
     5  1
     6  2
     7  3
     8  0
     9  1
    10  2
    11  3
    12  0
    13  1
    14  2
    15  3

> It's also more difficult to explain to children.

And rewarding, unless you want your children to grow up innumerate.

if the stopwatch uses base 10, the last digit will be in the range [0, 9], making n >=10 irrelevant. in this range, 0 and 1 appear 3 times; 2 and 3 appear 2 times.

if the stopwatch uses hex, then 0-3 will appear equally often in this case

The second digits on my digital watches extend to 59, and if a precocious youngster were to correctly object that a limit of 59 produces a bias, I would extend the range by multiplying the minute digit by 60 and adding it to the seconds (thus reducing the bias). We are, after all, most likely using a calculator to produce the result.

> if the stopwatch uses hex ...

I think we're safely in the red herring zone now. :)

EDIT: Yes, of course -- when confronted by a correct and reasoned reply, downvote it to discourage any such mistakes in the future.

i think you're confused on what a 'last digit' is. the seconds digits (plural) contain two digits, which range from 0-59; the last digit (singular) ranges from 0-9

> i think you're confused on what a 'last digit' is.

Digits, not digit, please, and do try to limit the anti-intellectualism and adversarial posture.

The last digit on the clock can only be 0 through 9. If you truncate your chart accordingly, 0 and 1 are represented more than 2 and 3. Or do you mean “the entire seconds value” (for which this idea would work with four children) instead of “the last digit”?

To avoid confusion, I used the expression "last digits".

It actually doesn't matter how many options are in your random number generator. You only get a normal distribution if the number of children you have divides the number of options in your generator. Even if you're using the seconds of a clock, it doesn't work for 7 children.

> It actually doesn't matter how many options are in your random number generator.

It certainly does -- the larger the random number, the fairer the outcome is.

> Even if you're using the seconds of a clock, it doesn't work for 7 children.

For a digits range of 0 - 59? Plus the fallback in the face of a precocious child of adding the number of minutes * 60?

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