Visualising and representing

A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

How efficiently can various flat shapes be fitted together?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

How many different colours of paint would be needed to paint these pictures by numbers?

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Can you explain why every year must contain at least one Friday the thirteenth?

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?