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(Moving Counter Problem)
It has been suggested that this puzzle was a great favourite among the
young apprentices of the City of London in the sixteenth and seventeenth
centuries. Readers will have noticed the curious brass grasshopper on
the Royal Exchange. This long-lived creature escaped the fires of 1666
and 1838. The grasshopper, after his kind, was the crest of Sir Thomas
Gresham, merchant grocer, who died in 1579, and from this cause it has
been used as a sign by grocers in general. Unfortunately for the legend
as to its origin, the puzzle was only produced by myself so late as the
year 1900. On twelve of the thirteen black discs are placed numbered
counters or grasshoppers. The puzzle is to reverse their order, so that
they shall read, 1, 2, 3, 4, etc., in the opposite direction, with the
vacant disc left in the same position as at present. Move one at a time
in any order, either to the adjoining vacant disc or by jumping over one
grasshopper, like the moves in draughts. The moves or leaps may be made
in either direction that is at any time possible. What are the fewest
possible moves in which it can be done?

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