5. I have only found one solution excluding
reflections and rotations:
6. You have six beads placed in a plane.
The object is to find two pairs of equidistant
beads. (In other words, find a pair of beads
that are exactly the same distance apart as
another pair of beads).
The distance between two beads is meant as
the distance between their centers.
7.
8.
9. In the diagram below, each circle is just big
enough to touch all four sides of the square. The
area of the square is therefore just a bit more
than the area of one of the circles.
I want to know how many of the circles you need
to cover the whole square. Is 2 enough? Or do
you need 3? Or 4? Or more?
I have put 5 circles for you to play with (print and
then cut them out), but what is the least number
you need?
10.
11. But because it is so difficult to cut out the circles accurately
enough to see the tiny gaps that appear, you can be happy if
you answered three circles. But four is correct, and you can
actually use a program like "GeoGebra" to solve it.
12. There are nine compositions (A to I) of eight colored cubes.
Find two identical compositions. They can be rotated.
13.
14. There are five squares (one 3x3 and four 1x1) formed with 20
matchsticks, as shown in the illustration. Move two
matchstick to get seven squares. Overlapping or breaking of
matchsticks or "loose ends" are not allowed.
15.
16. Seven matchsticks form two squares as shown in the
illustration. Move three matchsticks to get three squares. You
can rotate matchsticks, but you can't overlap and/or damage
them
17.
18. The figure below represents two equal squares placed side by
side. The second square has been cut in half diagonally: The
puzzle is to cut the figure into four identical pieces (the
pieces may be flipped over).
19. Give the square a side length of two units, then the figure has
an area of six square units (4 + 2). One quarter of this is 1.5
square units, which suggests the solution given
20. This picture was made up from four squares
stuck one upon another. I am sure you can
see how it was made.
In the diagrams below are some more pictures
made from overlapping squares.
21. Can you work out how they were made? In other words,
which square was placed 1st (on the bottom), which
was 2nd, etc?
22. The numbers in the diagrams show the order of the
squares, from the bottom (1) to the top.
23. Place 10 balls in 5 lines
in such a way that each line
has exactly 4 balls on it.
