Your Solutions - Stage 3 & 4

Network Trees

Age 14 to 18
Challenge Level

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

Maxi Pyramid

Age 11 to 16
Challenge Level

What is the largest number you can obtain at the top of this pyramid?

Positive Differences

Age 11 to 16
Challenge Level

Can you fill the circles with the numbers 1 to 6?

11x11 Square

Age 11 to 16
Challenge Level

Here's a neat trick you can do with an 11 by 11 square...

River Crossing

Age 11 to 18
Challenge Level

There is nothing half so much worth doing as simply messing about in boats...

Isosceles Seven

Age 14 to 16
Challenge Level

Is it possible to find the angles in this rather special isosceles triangle?

Iffy Logic

Age 14 to 18
Challenge Level

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

IFFY Triangles

Age 14 to 18
Challenge Level

Can you prove these triangle theorems both ways?

The Tour De Clochemerle

Age 14 to 18
Challenge Level

Can you work out where these 5 riders came in a not-quite-so-famous bike race?

Circumference Angles

Age 11 to 16
Challenge Level

Can you prove the angle properties described by some of the circle theorems?

Cyclic Quadrilaterals Proof

Age 11 to 16
Challenge Level

Can you prove that the opposite angles of cyclic quadrilaterals add to $180^\circ$?

Pythagoras Proofs

Age 11 to 16
Challenge Level

Can you make sense of these three proofs of Pythagoras' Theorem?

Matter of Scale

Age 14 to 16
Challenge Level

Can you prove Pythagoras' Theorem using enlargements and scale factors?

Overlap

Age 14 to 16
Challenge Level

A red square and a blue square overlap. Is the area of the overlap always the same?

Pentakite

Age 14 to 18
Challenge Level

Given a regular pentagon, can you find the distance between two non-adjacent vertices?

Quad in Quad

Age 14 to 18
Challenge Level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?