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?
Each frieze pattern is formed by repeating copies of one small
bit of the pattern (the motif) over and over again by translation,
rotation and reflection. Sort the frieze patterns into seven pairs
according to the way in which the motif is repeated. Explain how
you match the pairs.