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 ;).