order without doing this, or using
any actual cards.

12.--_The Merchant's Puzzle._

Of the Merchant the poet writes, "Forsooth he was a worthy man withal."
He was thoughtful, full of schemes, and a good manipulator of figures.
"His reasons spake he eke full solemnly. Sounding away the increase of
his winning." One morning, when they were on the road, the Knight and the
Squire, who were riding beside him, reminded the Merchant that he had not
yet propounded the puzzle that he owed the company. He thereupon said,
"Be it so? Here then is a riddle in numbers that I will set before this
merry company when next we do make a halt. There be thirty of us in all
riding over the common this morn. Truly we may ride one and one, in what
they do call the single file, or two and two, or three and three, or five
and five, or six and six, or ten and ten, or fifteen and fifteen, or all
thirty in a row. In no other way may we ride so that there be no lack of
equal numbers in the rows. Now, a party of pilgrims were able thus to
ride in as many as sixty-four different ways. Prithee tell me how many
there must perforce have been in the company." The Merchant clearly
required the smallest number of persons that could so ride in the
sixty-four ways.

[Illustration]

13.--_The Man of Law's Puzzle._

The Sergeant of the Law was "full rich of excellence. Discreet he was,
and of great reverence." He was a very busy man, but, like many of us
to-day, "he seemed busier than he was." He was talking one evening of
prisons and prisoners, and at length made the following remarks: "And
that which I have been saying doth forsooth call to my mind that this
morn I bethought me of a riddle that I will now put forth." He then
produced a slip of vellum, on which was drawn the curious plan that is
now given. "Here," saith he, "be nine dungeons, with a prisoner in every
dungeon save one, which is empty. These prisoners be numbered in order,
7, 5, 6, 8, 2, 1, 4, 3, and I desire to know how they can, in as few
moves as possible, put themselves in the order 1, 2, 3, 4, 5, 6, 7, 8.
One prisoner may move at a time along the passage to the dungeon that
doth happen to be empty, but never, on pain of death, may two men be in
any dungeon at the same time. How may it be done?" If the reader makes a
rough plan on a sheet of paper and uses numbered counters, he will find
it an interesting pastime to arrange the prisoners in the fewest possible
moves. As th