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Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

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}.

Sums of Pairs

Age 11 to 16 Challenge Level:
See the Teachers' Notes to Arithmagons for a possible approach to working with an essentially identical problem.