### Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

### Tree Graphs

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.

### Magic Caterpillars

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

# Neural Nets

##### Stage: 5

Published September 2012.

Perceptrons and feedback circuits

In standard mathematical logic, a logic gate activates, or 'fires' depending on whether certain inputs are either ON of OFF

Example of a logical AND gate.

In an artificial neural network, this concept is extended: inputs can carry differing levels of current so that a gate (neurone) fires provided that the overall input level exceeds a certain threshold.

For what ranges of input levels will these neurones fire?

SOME EXAMPLES

SOME PROBLEM WITH XOR

A feedback circuit

ACTIVATION FUNCTION -- SIGMOIDS