(algorithmic) Sorting Hat

[regant4]

No: HPFGUIDX 38069

--- In HPforGrownups at y..., "mike_wiltse" <mike_wiltse at y...> wrote:
> ...
> Lets asume 28 new kids were starting school, and all 28 students 
> would fit perfectly into Gryfindor.  The hat would not put them 
all 
> there.  Its job is to sort them into 4 houses first.  People who 
know 
> where the want to go and fit the profile take very little effort.  
> Where as people who dont know where they want to be, and dont 
> imidiatly fit one profile take longer.  
> ...

Would this work in a single pass (as the Sorting Hat makes)? Suppose 
of the 28 new students, all of whom would perfectly fit into 
Gryfindor, the last 10 are heirs of Gryfindor himself (Ron's future 
younger brothers – dectets ;-). By the time the hat gets to them 
Gryfindor is already full, or nearly so, and they have to be put in 
other houses! Surely some mistake.

So either 
1) The intake is so large that such anomalies are very unlikely (I 
think JKR says that Hogwarts has over a thousand students)
2) The sorting hat is magic
3) The sorting hat gets a sneak look at the students as they arrive 
and so can guess the numbers falling into each house, and set its 
house boundaries accordingly to balance numbers.

I believe it is magic, and that it assigns students to the houses 
they will flourish in. If in an odd year everyone ends up in 
Hufflepuff, then the school has to live with that.