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Age 14 to 16
Challenge Level 
This problem gives opportunities to address processes that need
splitting into parts.
The path of the light ray switches direction at intervals, and handling that is crucial to the problem.
The path of the light ray switches direction at intervals, and handling that is crucial to the problem.
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DOTS Division
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Sixational
The nth term of a sequence is given by the formula n^3 + 11n. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by 6.