What would be the smallest number of moves needed to move a Knight
from a chess set from one corner to the opposite corner of a 99 by
99 square board?
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
This rectangle is cut into five pieces which fit exactly into a
triangular outline and also into a square outline where the
triangle, the rectangle and the square have equal areas.
Can you cut up any triangle, using straight cuts, and rearrange
the pieces to make a rectangle and a square?
Start by just investigating triangles which have a height of less
than twice the base but greater than half the base. Make your own
puzzle from card by cutting the triangle into a small number of
pieces that can be re-arranged into a rectangle and into a square
with the same area.
Suppose you have two triangles with the same area. Do you think
you can cut one into pieces which can be re-arranged to form the