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Middle Man

Age 16 to 18
Challenge Level Yellow star
  • Problem
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Mark a point $P$ inside a closed curve.

Is it always possible to find two points that lie on the curve, such that $P$ is the mid point of the line joining these two points?


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A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?

Be Reasonable

Prove that sqrt2, sqrt3 and sqrt5 cannot be terms of ANY arithmetic progression.

OK! Now Prove It

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?

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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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