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Rule of Three

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

Cereal Mix

Age 11 to 14
Challenge Level

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars.

The ingredients cost:

  • dried apricots $ £7$ per kg

  • nuts $ £6$ per kg

  • seeds $ £4$ per kg

He has been asked to supply a mix which costs $ £5$ per kg.

What combination of ingredients could he supply?

Is there a relationship between the amounts of each ingredient that he could supply?


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.
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