This puzzle dates back to the beginning of the 20th century, and since
then it was many times produced as an advertising puzzle. The goal is to
make of these four pieces a symmetric capital T. You're allowed to rotate
the pieces as you wish and even turn them over, but they must not overlap
each other in the final letter. In fact there are two symmetric capital T
letters that you can get from these pieces. Try to find both of them. By
the way, there is at least one more extra symmetric shape that can be
formed from this set - isosceles trapezoid. Can you find it too?

Three neighbors - the owners of the skyscraper, the bungalow and the
cottage - who share the small park, as shown in the illustration, have a
falling out. This led them to the decision to build three pathways from
their houses to the gates of the park (every path to another gate), so
that none of the paths cross each other! The owner of the skyscraper wants
to build the path to the central gate. The owner of the bungalow (on the
left) wants to make the path to the gate on the right, and the owner of
the cottage (on the right) wants to have his path to the left gate. The
colors of the lawns around the houses and the respective spots next to the
gates will help you to understand their plan. Please, notice that none of
the path can go behind the skyscraper (see the Top view). How do the
quarrelsome neighbors have to build their pathways?

Arrange the 4x4 match square grid as shown in the illustration. The object
of the puzzle is to remove nine matches so that no square (of any size)
will remain.

Draw the chess board shown in the topmost illustration or just print it
out. Place a chess knight (or a simple coin) in any cell of this board.
The object is to visit with the knight every cell of the board exactly
once, and return to the initial cell where your trip began from. Two
bottom diagrams, a and b, show some possible moves of the chess knight
which always moves either one cell in one direction, and then two cells in
another direction, or vice versa.

The four identical equilateral triangles can be arranged together to make
exactly the same equilateral triangle, only bigger, just as shown in the
upper left illustration. The object is to arrange the four shapes shown in
the center of the illustration into the same shape as one of those shapes
is, only bigger. You are allowed to rotate and flip the shapes as you wish
but the pieces are not allowed to overlap in the final shape.

A cube has six faces but does every net made up of six squares fold into a
cube? Just by looking at the seven patterns here, can you tell which ones
can be folded into a perfect cube box?

Bizarre shapes and strange connections make math interesting and nothing
is more strangely fascinating than the simplicity and topology of the
Mobius strip. The nineteenth-century German mathematician A. F. Mobius
discovered that it was possible to make a surface that has only one side
and one edge. Although such an object seems impossible to imagine, making
a Mobius strip is very simple: take a strip of ordinary paper and give one
end a twist, then glue the two ends together. And there it is. If you
begin drawing a line lengthwise down the strip, after one full revolution
you will be at the point where you started – but on the opposite side of
the strip! Drawing the line through another full revolution will find you
back at the beginning. Mobius strips are fun to play with, but industrial
engineers have made good use of the shape as well. Conveyor belts are
often designed as Mobius strips so that the surface wears out half as
fast..

Janet wants to join the three parts above into a bracelet. The jeweler
says he has to charge $2 for each link he must cut and resolder. He
figures it will cost $6. She figures out a way it will cost $4. How does
Janet solve the problem?

A father has three square lots for his four children. He wants to give
each child a piece of land to plant vegetables. How can he divide these
lots so each child gets a plot the same size and shape?