Mark a point P inside a closed curve. Is it always possible to find
two points that lie on the curve, such that P is the mid point of
the line joining these two points?
The triangle ABC is equilateral. The arc AB has centre C, the arc
BC has centre A and the arc CA has centre B. Explain how and why
this shape can roll along between two parallel tracks.
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it is facing the other way round.
My train left London between 6 a.m. and 7 a.m. and arrived in Paris
between 9 a.m. and 10 a.m. At the start and end of the journey the
hands on my watch were in exactly the same positions but the minute
hand and hour hand had swopped places. What time did the train
leave London and how long did the journey take?
A security camera, taking pictures each half a second, films a
cyclist going by. In the film, the cyclist appears to go forward
while the wheels appear to go backwards. Why?
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?