[net.math] Re. Splitting Candy Bars

rjs (10/20/82)

In order for n people to fairly split a candy bar, persons 1 through n-1
should each break off a piece which they consider to be 1/(n-p+1) of the
remaining length (p = person #).  Then person n chooses a piece, person
1 chooses a piece, person 2 chooses a piece, ... , person n-1 gets the
last piece.  It will be in each persons best interest to be as close as
possible to the correct size when breaking off a piece.

	I'm not afraid to split my name
	Robert
						Snyder

	floyd!rjs

cw (10/20/82)

Algorithm: How to Cut a Pie for N People

For N turns, perform the following steps.

1.  On turn i, the first remaining person cuts 1/N-th the 
    remaining pie.  This cut counts as a touch.

2.  Each remaining person has the opportunity (once) to REMOVE as much
    of the cut piece as desired.  Actual removal counts as a touch.

3.  The last person to touch the piece gets it.  That person is removed
    from the eligible people still.

This algorithm is fair because you only REMOVE some pie from a piece
if you
	a. think it really is too big, in which case if you are the
	   last you got a fair 1/N-th piece.
	b. because you are trying to make the piece too small; in
	   this case, if no one else touches the piece, you get your
	   just desserts.

Charles

PS.  I can spell.