slender than any one of the pieces employed. It is really an optical
illusion. Again, notice in the case of the yacht (14) how, by leaving
that little angular point at the top, a complete mast is suggested. If
you place your Tangrams together on white paper so that they do not
quite touch one another, in some cases the effect is improved by the
white lines; in other cases it is almost destroyed.

[Illustration: 11]

[Illustration: 12]

Finally, I give an example from the many curious paradoxes that one
happens upon in manipulating Tangrams. I show designs of two dignified
individuals (15 and 16) who appear to be exactly alike, except for the
fact that one has a foot and the other has not. Now, both of these
figures are made from the same seven Tangrams. Where does the second man
get his foot from?

[Illustration: 13]

[Illustration: 14]

[Illustration: 15]

[Illustration: 16]

PATCHWORK PUZZLES.

"Of shreds and patches."--_Hamlet_, iii. 4.

170.--THE CUSHION COVERS.

[Illustration]

The above represents a square of brocade. A lady wishes to cut it in
four pieces so that two pieces will form one perfectly square cushion
top, and the remaining two pieces another square cushion top. How is she
to do it? Of course, she can only cut along the lines that divide the
twenty-five squares, and the pattern must "match" properly without any
irregularity whatever in the design of the material. There is only one
way of doing it. Can you find it?

171.--THE BANNER PUZZLE.

[Illustration]

A Lady had a square piece of bunting with two lions on it, of which the
illustration is an exactly reproduced reduction. She wished to cut the
stuff into pieces that would fit together and form two square banners
with a lion on each banner. She discovered that this could be done in as
few as four pieces. How did she manage it? Of course, to cut the British
Lion would be an unpardonable offence, so you must be careful that no
cut passes through any portion of either of them. Ladies are informed
that no allowance whatever has to be made for "turnings," and no part of
the material may be wasted. It is quite a simple little dissection
puzzle if rightly attacked. Remember that the banners have to be perfect
squares, though they need not be both of the same size.

172.--MRS. SMILEY'S CHRISTMAS PRESENT.

Mrs. Smiley's expression of pleasure was sincere when her six
granddaughters sent to her, as a Christmas present, a very