Visualising and representing

A 3×3×3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Which hexagons tessellate?

Jack and Jill run at different speeds in opposite directions around the maypole. How many times do they pass in the first minute?

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

Can you form this 2010-digit number...

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

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