Rotations

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

How did the the rotation robot make these patterns?

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?

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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.

Points off a rolling wheel make traces. What makes those traces have symmetry?

Can you describe what happens in this film?