Visualising - October 2007, Stage 4&5

Problems

problem icon

The Perforated Cube

Stage: 4 Challenge Level: Challenge Level:1

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

problem icon

Spotting the Loophole

Stage: 4 Challenge Level: Challenge Level:1

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

problem icon

Making Tracks

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

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

problem icon

One Out One Under

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

problem icon

Sextet

Stage: 5 Challenge Level: Challenge Level:1

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

problem icon

Interpenetrating Solids

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!

problem icon

Cheese Cutting

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?

problem icon

Solving the Net

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Takes you through the systematic way in which you can begin to solve a mixed up Cubic Net. How close will you come to a solution?