this month, Stage 3 & 4

February 2003

 

Problems

problem Icon

Icosian Game

Stage:3 Challenge Level:Challenge Level:1

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only– returning to the vertex you started at.

problem Icon

Squares

Stage:3 Challenge Level:Challenge Level:1

Three dimensions is the theme within the main body of the magazine and although 3D LOGO does exist few appear to use it. However, within the confines of the plane a representation of space can be. . . .

problem Icon

All in the Mind

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

problem Icon

Marbles in a Box

Stage:3 Challenge Level:Challenge Level:2Challenge Level:2

You have 27 transparent unit cubes arranged in a 3 by 3 by 3 array. Marbles are alternately placed into the cubes by two players. How many unique winning lines of three marbles are possible?

problem Icon

Cubist Cuts

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

problem Icon

Cutting a Cube

Stage:3 Challenge Level:Challenge Level:3Challenge Level:3Challenge Level:3

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

problem Icon

Excel Investigation: Happy Numbers

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

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Use a spreadsheet to investigate this sequence.

problem Icon

Excel Interactive Resource: Equivalent Fraction Bars

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

A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.

problem Icon

Excel Technique: LOOKUP Functions

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

Learn how to use lookup functions to create exciting interactive Excel spreadsheets.

problem Icon

In a Spin

Stage:4 Challenge Level:Challenge Level:2Challenge Level:2

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

problem Icon

Magic Caterpillars

Stage:4 and 5 Challenge Level:Challenge Level:1

Put numbers 1 to n on the edges and vertices of a graph so that the sum of the numbers on a vertex and on all arcs joined to that vertex is the same for all vertices.

problem Icon

Plum Tree

Stage:4 and 5 Challenge Level:Challenge Level:1

Label a graph with the numbers 1 to n, one on each vertex, one on each arc. A Totally Magic graph is both Edge Magic and Vertex Magic.