Digits, not digit. I doubt this fact will limit the number of airheads who downvote posts containing useful content.
> If the last digit is 20, and there are four children, the result is 4 * 20 / 10 = 8.
Singular "digit."
Look -- I posted the obvious solution to a common problem. Everything else depends on those who can't stand the unwelcome intrusion of simple, easily stated facts.
My "attitude" is that this problem is easily solved, using simple arithmetic. Imagine you're a scientist -- as such, do you object to a useful result because of its source?
You posted a solution that was less correct than the solution you were responding to.
The solution I originally posted is fair and practical. Divide the digits as evenly as you can between the kids, and treat any extras as a do-over. While it's technically possible to never end, in practical terms it produces a fair result within ten seconds. (The fact that you're trying to "fix" this solution confuses me; I wonder if perhaps you didn't understand it in the first place and have been arguing based on a misunderstanding ever since.) By contrast, your solution does not produce a fair result for certain numbers of kids. I promise, the kids in my family would have discovered that bias by the time there were 7 of us.
> "can't stand the unwelcome intrusion of simple, easily stated facts"
One of the reasons you've gotten a lot of downvotes here is because of the combination of:
- posting an incorrect solution
- insisting the incorrect solution is correct, in spite of several people showing you why it is not, and
- complaining that people who are downvoting are the ones in the wrong, including several insults (calling people airheads, innumerate, brainless cyberwarriors, saying they can't stand simple facts, etc.)
At times I really enjoy your comments. I've sent a lot of upvotes your way over the years. But in this case you're wrong, and you've taken to insulting the people who are patiently trying to explain to you why you're wrong. I know you're capable of better. Please take the time to reread and understand the original solution, and stop insulting people.
When you get a downvote, ignore it. It's probably accidental or meaningless and these tend to self correct over a day.
When people downvote a bunch of your posts in a thread IGNORE THE DOWNVOTES. Vindictive downvote sprees are usually corrected over the course of the day. Mentioning the downvotes will usually prevent those corrective upvotes. Me tioning the downvotes in the unpleasant way that you do will attract downvotes.
You may wish to consider how you're presenting the information. If the first table of numbers gets downvotes posting the same table again without more information is going to get the same downvotes.
You could argue that it should not be this way, but it is.
Indeed it is. State facts, back up what you say with evidence, get downvoted. As certain as sunrise.
> If the first table of numbers gets downvotes posting the same table again without more information is going to get the same downvotes.
The alternative is to adopt the standards of religion instead of science. In religion, if you start losing followers, you change the mythology. In science, evidence is evidence, and how people feel about it has no standing.
> When you get a downvote, ignore it. It's probably accidental or meaningless ...
Easily proven false. My downvotes inevitably accompany anything I post that has evidence and/or links to references. If I offer an uncorroborated opinion or philosophical remark, however irrelevant or baseless, it's treated neutrally. This is how science works -- you observe things dispassionately and don't let yourself to be swayed by what people think is true.
Do you disagree with any of the following statements, and if yes, where and why?
- original stopwatch solutions gives equal probability for any of the kid to get picked
- your modulo solution does not give equal probability for any of the kid to get picked
- you argue that the non-uniformness of your solution is not relevant in practice, because number of kids is likely to be an order of magnitude smaller than the readout from the stopwatch (i.e. last two digits)
Okay. I usually expect people to locate the errors in their own thinking, but in this case, I'll make an exception. Here's one of the suggestions: "multiply the last digit by the number of children and divide by ten". Let's see how this works out:
n n * 7 / 10
----------------
0 0
1 0
2 1
3 2
4 2
5 3
6 4
7 4
8 5
9 6
I'm going to avoid your straw men, with this exception:
> you argue that the non-uniformness of your solution is not relevant in practice
I never said that. I said that the error could be minimized. But consider my test of the the alternative listed above. The error inherent with a relatively small number of children and a relatively large original number, say, 0 - 59, is a smaller error than the proposed alternative.
Hey, I asked you three simple questions with pretty much boolean answers, in order to try and clarify where exactly you end up disagreeing with everyone. Please be charitable.
> Here's one of the suggestions: "multiply the last digit by the number of children and divide by ten".
Hey, that one was clearly meant as a joke, and is not the suggestion I was referring to. If something is a strawman here, this is. The one I asked about is the "My parents used the last digit on a stopwatch to decide which of the kids got to pick the radio station in the car and similarly trivial decisions. (If 0-9 couldn't be divided evenly among the kids present, leftover digits would result in a re-roll.)".
In light of that, could you provide the answers?
Anyway, I must say I found the technique I used above quite effective at figuring out continous disagreements. You state some simple true/false statements describing your assumptions and ask the other party to agree/disagree and explain the points of disagreement. Apply recursively if needed. Kind of a discussion equivalent of git bisect ;).
With a single generation, you can't uniformly choose from a set of n options with a random number generator that outputs m options, unless n divides m.