this month, Stage 3 & 4

July 1999

 

Problems

problem Icon

Weighty Problem

Stage:3 Challenge Level:Challenge Level:1

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

problem Icon

Alphabet Soup

Stage:3 Challenge Level:Challenge Level:1

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

problem Icon

First Forward Into Logo 1

Stage:2, 3 and 4 Challenge Level:Challenge Level:1

A Short introduction to using Logo. This is the first in a twelve part series.

problem Icon

LOGO Challenge 1 - Star Square

Stage:2, 3 and 4 Challenge Level:Challenge Level:1

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

problem Icon

Lower Bound

Stage:3 Challenge Level:Challenge Level:1

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

problem Icon

Pinned Squares

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

The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .

problem Icon

Pie Cuts

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

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

problem Icon

Bang's Theorem

Stage:4 Challenge Level:Challenge Level:1

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

problem Icon

Plus Minus

Stage:4 Challenge Level:Challenge Level:1

Without using a calculator evaluate (a) 7778^2 - 2223^2 (b) 888889^2 - 111112^2