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A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?


The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and two sides of the triangle. If the small circle has radius 1 unit find the radius of the larger circle.

Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Surprising Transformations

Age 14 to 16
Challenge Level
You may want to have a look at Translating Lines and Reflecting Lines before working on this problem.

Think about what happens to the intercept and gradient after each transformation.

How can I combine these transformations so that the gradient stays the same and the intercept moves down 9 places?