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Amusements in Mathematics

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.
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