Visualising and representing

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

Can you find the time between 3 o'clock and 10 o'clock when my digital clock looks the same from both the front and back?

Every third page number in this book has been omitted. Can you work out what number will be on the last page?

How does the perimeter change when we fold this isosceles triangle in half?

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?

What does Pythagoras' Theorem tell you about the radius of these circles?

Can you make the numbers around each face of this solid add up to the same total?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.