I happened to see a little girl sorting out some jam in a cupboard for
her mother. She was putting each different kind of preserve apart on the
shelves. I noticed that she took a pot of damson in one hand and a pot
of gooseberry in the other and made them change places; then she changed
a strawberry with a raspberry, and so on. It was interesting to observe
what a lot of unnecessary trouble she gave herself by making more
interchanges than there was any need for, and I thought it would work
into a good puzzle.
It will be seen in the illustration that little Dorothy has to
manipulate twenty-four large jampots in as many pigeon-holes. She wants
to get them in correct numerical order--that is, 1, 2, 3, 4, 5, 6 on the
top shelf, 7, 8, 9, 10, 11, 12 on the next shelf, and so on. Now, if she
always takes one pot in the right hand and another in the left and makes
them change places, how many of these interchanges will be necessary to
get all the jampots in proper order? She would naturally first change
the 1 and the 3, then the 2 and the 3, when she would have the first
three pots in their places. How would you advise her to go on then?
Place some numbered counters on a sheet of paper divided into squares
for the pigeon-holes, and you will find it an amusing puzzle.
[Illustration]