Toughnuts - Try These Unsolved Problems

Make Those Braceletslive

Age 7 to 11
Challenge Level

Find all the ways of arranging the beads on this bracelet, using just two colours.

Sliding Rectangleslive

Age 11 to 16
Challenge Level

Which of the two rectangles has the greater area?

Iffy Logiclive

Age 14 to 18
Challenge Level

Can you rearrange the cards to make a series of correct mathematical statements?

Network Trees

Age 14 to 18
Challenge Level

Explore some of the different types of network, and prove a result about network trees.

A Frosty Puddlelive

Age 16 to 18
Challenge Level

Can you draw a sketch of how Frosty's volume changes as his height decreases?

Solving by Squaringlive

Age 16 to 18 Short
Challenge Level

Which of the statements is true?

Inequalities

Age 16 to 18
Challenge Level

Which of the statements must be true?

Two Cubic Equationslive

Age 16 to 18 Short
Challenge Level

Which statement correctly describes the real roots of the equation?

Mind Your Ps and Qslive

Age 16 to 18
Challenge Level

Sort these mathematical propositions into a series of 8 correct statements.

Dodgy Proofs

Age 16 to 18
Challenge Level

These proofs are wrong. Can you see why?

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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