ous wizard. The
interview had to do with an affair of the heart; but after the man of
magic had foretold the most favourable issues, and concocted a
love-potion that was certain to help his visitor's cause, the
conversation drifted on to occult subjects generally.

[Illustration]

"And art thou learned also in the magic of numbers?" asked the knight.
"Show me but one sample of thy wit in these matters."

The old wizard took five blocks bearing numbers, and placed them on a
shelf, apparently at random, so that they stood in the order 41096, as
shown in our illustration. He then took in his hands an 8 and a 3, and
held them together to form the number 83.

"Sir Knight, tell me," said the wizard, "canst thou multiply one number
into the other in thy mind?"

"Nay, of a truth," the good knight replied. "I should need to set out
upon the task with pen and scrip."

"Yet mark ye how right easy a thing it is to a man learned in the lore of
far Araby, who knoweth all the magic that is hid in the philosophy of
numbers!"

The wizard simply placed the 3 next to the 4 on the shelf, and the 8 at
the other end. It will be found that this gives the answer quite
correctly--3410968. Very curious, is it not? How many other two-figure
multipliers can you find that will produce the same effect? You may place
just as many blocks as you like on the shelf, bearing any figures you
choose.

83.--_The Ribbon Problem._

[Illustration]

If we take the ribbon by the ends and pull it out straight, we have the
number 0588235294117647. This number has the peculiarity that, if we
multiply it by any one of the numbers, 2, 3, 4, 5, 6, 7, 8, or 9, we get
exactly the same number in the circle, starting from a different place.
For example, multiply by 4, and the product is 2352941176470588, which
starts from the dart in the circle. So, if we multiply by 3, we get the
same result starting from the star. Now, the puzzle is to place a
different arrangement of figures on the ribbon that will produce similar
results when so multiplied; only the 0 and the 7 appearing at the ends of
the ribbon must not be removed.

84.--_The Japanese Ladies and the Carpet._

[Illustration]

Three Japanese ladies possessed a square ancestral carpet of considerable
intrinsic value, but treasured also as an interesting heirloom in the
family. They decided to cut it up and make three square rugs of it, so
that each should possess a share in her own house.