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:

Jo has three numbers which she adds together in pairs.

When she does this she has three different totals: $11$, $17$ and $22$

What are the three numbers Jo had to start with?

Can you describe a method that would enable you to work out the three numbers given any three totals?

Calculus generally. Making and proving conjectures. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Generalising. 2D shapes and their properties. Inequalities. Polynomial functions and their roots. Trial and improvement. Working systematically.

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Days and Dates

Diophantine N-tuples

DOTS Division

Sums of Pairs

Age 11 to 16 Challenge Level: