Dividing pie between N children

Kathy,

I think this works, in theory at least. Suppose you have N children ... (of course if N is large you have bigger problems than dividing up the pie) ... but anyway, assume that each child wants to be sure that no-one ends up with a bigger piece of pie than them. The following procedure should work:

The first child cuts a segment (a slice) of pie, but does not remove it.
The second child makes a cut
The third child makes a cut
and so on until
The N-1 th child makes a cut.

That's the end of the cutting

The Nth child then selects a piece
Then the N-1 th child selects a piece
Then the N-2 th child
and so on until
The first child gets the final piece

This should work because:
if any of the first N-1 children makes a bad decision, then the Nth child ends up with a bigger piece than anybody.

if any of the first N-2 children makes a bad decision then one or both of the N-1 th and Nth children will get a bigger piece of pie than anybody else

and so on!

To make this work in practice it would be best to arrange your children round the table in descending order of ability to estimate sizes of pieces of pie.
Child number 1 has the most difficult decision to make -- child number N has the easiest.

This is probably more than you wanted to know -- but it's an intriguing problem.
If you ever try it, please let me know.

Martin