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A Little Light Thinking
Age 14 to 16
Challenge Level 
The problem Shifting Times Tables offers an introductory challenge for exploring linear sequences.
The problem Remainders explores some properties of numbers which could be useful when thinking about this problem.You may also like
Polycircles
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
Pick's Theorem
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Producing an Integer
Multiply a sequence of n terms together. Can you work out when this product is equal to an integer?