# December 2002, Stage 2&3

## Problems

### The Third Dimension

##### Stage: 1 and 2 Challenge Level:

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

### A Puzzling Cube

##### Stage: 2 Challenge Level:

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

### Inside Seven Squares

##### Stage: 2 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

### Square Corners

##### Stage: 2 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

### LOGO Challenge - Triangles

##### Stage: 3 Challenge Level:

Make some triangular patterns in LOGO

### Coloured Edges

##### Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

### Covering Cups

##### Stage: 3 Challenge Level:

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

### Triangular Tantaliser

##### Stage: 3 Challenge Level:

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

### Sums of Pairs

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

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

### Instant Insanity

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

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.