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  • Early Years Foundation Stage

Chocolate 2010

Age 14 to 16
Challenge Level Yellow star
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This looks like a fairly standard problem leading to a simple algebraic equation that can be solved, however the need to examine what is happening to each of the digits of the number means that the solution requires a little more thought and an appreciation of place value.

Being able to generalise this to any year may help convince you that the structure of the problem is understood.

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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}.

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.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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