# Visualising - Upper Secondary

### Cops and Robbers

##### Stage: 2, 3 and 4 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

### Air Nets

##### Stage: 2, 3, 4 and 5 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

### Blockupied

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 28 - 2007
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

### Sliding Coins

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 43 - 2007
The diagram shows 10 identical coins which fit exactly inside a wooden frame. What is the largest number of coins that may be removed so that each remaining coin is still unable to slide.

### Gaudi's Design

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 12 - 2015
Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?

##### Stage: 3 and 4 Short Challenge Level:

Weekly Problem 46 - 2007
When a solid cube is held up to the light, how many of the shapes shown could its shadow have?

### Semicircular Design

##### Stage: 4 Short Challenge Level:

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

### Building Tetrahedra

##### Stage: 4 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

### Attractive Tablecloths

##### Stage: 4 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

### Out of the Window

##### Stage: 4 Short Challenge Level:

Weekly Problem 3 - 2012
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

### Vector Journeys

##### Stage: 4 Challenge Level:

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

### In or Out?

##### Stage: 4 Short Challenge Level:

Weekly Problem 52 - 2014
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

### Trisected Triangle

##### Stage: 4 Short Challenge Level:

Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

### Cubic Net

##### Stage: 4 and 5 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

### Coordinated Crystals

##### Stage: 5 Challenge Level:

Explore the lattice and vector structure of this crystal.