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Topic: Manually sample from [1,2,...N] with no pencil/paper/electronics
Replies: 1   Last Post: Mar 1, 2014 9:53 PM

 Ben Bacarisse Posts: 1,972 Registered: 7/4/07
Re: Manually sample from [1,2,...N] with no pencil/paper/electronics
Posted: Mar 1, 2014 9:53 PM

andymhancock@gmail.com writes:

> On Friday, February 28, 2014 9:34:39 AM UTC-5, Ben Bacarisse wrote:
>> andymhancockATgmail.com writes:
<snip>
>>> Bob practices in the sport of Fitzy Ball. He rotates around to a
>>> particular training routine once every few weeks, but it may be
>>> plus/minus so many days. There are (say) 3 spots in the training
>>> routine where things can be varied. Basically, he can choose one
>>> of Ni segment variations at each spot i (i=1 to 3), yielding
>>> M=N1xN2xN3 possible variations of the training routine. If he
>>> doesn't want to neglect any of the M routines, he needs a scheme to
>>> randomly choose one of Ni segment variations with near equal
>>> probability at each spot i. At the time when these choices are
>>> being made, he will likely not have pencil/paper or electronic
>>> device. He will know the day of the week, and likely the day of
>>> the month.

<snip>
>> The fairest selection scheme is just some permutation of the set of
>> triples (1,1,1), (1,1,2), ... (N1, N2, N3). This would require
>> picking a number between 0 an M! and using that to generate the
>> permutation. Computers can do this, but not (most) humans!

>
> I might be misunderstanding, but there are a total of M=N1xN2xN3
> different routines that can be generated, so wouldn't you (or Bob)
> choose a number from 1 to M? Actually, the example numbers I gave are
> real. N1=2, N2=4, and N3=2.

There are M routines, so a perfectly fair set of training routines does
each of the them M routines in some order. That's M!.

>> But you don't say that the sequence must be arbitrary.
>
> It can be arbitrary. And either deterministic or random, but it must
> not rely on keeping track of a state. It can make use of readily
> available info like the date and day of week.

That's a matter of definition. The date in part of the state of the
world -- certainly part of the state of Bob's mind. It seems an
arbitrary distinction to rule out using any knowledge of previous
actions, but it's your specification so you can do that if you want.

>> If Bob can remember a three-digit number he can just "increment" the
>> previous one and do that routine today. The increment is a little
>> non-standard since it's probably simpler to have no zeros, and, to
>> avoid having to remember the various Ni, you'd write the number with
>> the least significant digit first. In effect, you just have to
>> remember what you did yesterday and do the next routine today.

>
> It's once every few weeks, and it can't rely on accessing a state
> information of any kind that has been kept somewhere.

The date is information that has to be kept somewhere is it not -- in
Bob's head, in a calendar, on a piece of paper...? But I accept your
constraint that remembering a number is not an option -- my suggestion
is not suitable.

<snip>
--
Ben.