Visualising and representing

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves it will take to move the red counter to HOME?

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

Can you find a rule which connects consecutive triangular numbers?

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?

Can you mark 4 points on a flat surface so that there are only two different distances between them?

A huge wheel is rolling past your window. What do you see?