And then an unusual method of "counting by partitions" that
Patricia Baggett and Andrzej Ehrenfeucht proposed at the 2011 National Math Meetings.
They proposed that primitive societies may have counted
this way. Let's suppose you need to let the King know how many
sheep you have:
divide your sheep equally ("one for you, one for me") into two pens: either there is one left over, or not. You make a note of whether there is one left over or not.
Send all the sheep in pen two (and any "left over") out to pasture, and then
You divide the sheep in pen one into pens one and two: i.e., just do it again! And again, and again, and.... until you get down to a pen one with just sheep in it.
Now let's see how we might record the results to send to the King.
9 sheep
22 sheep
54 sheep
The easy way to do this is via a tree (see this webpage for the example of 22).
