Home 

Senior Challenge 4

We cannot guarantee how well this page  will print, so click here to open a pdf version for printing if you need it. There are applets for Questions 2 and 3. These can be activated by clicking on the appropriate diagrams in the questions.

Question 1: Make Magic

 

We cut up a magic square into these 10 tiles and now we can’t remember how to put them back into position.

Are there any naturally mathematical people out there who can help us?

 

 

Question 2: Wallpaper Patterns on a Grid

When you place the grids of Challenge 4, Question 2, side by side, you make a wallpaper pattern. Here’s what happens when Patterns A and B are repeated again ad again.

As you can see, you only have to give a quarter turn to the wallpaper made by Pattern A and it is the same as the wallpaper made by Pattern B.

The Challenge

What different wallpaper patterns can you make by repeating the patterns that can be made on a 4×4 grid?

(Hard but worth a try) What different wallpaper patterns can be made if you start with a 5×5 grid?

Please note: There is an applet to help you with this question. Click on the diagram to open it.

 

 

Question 3: Numbers in Boxes

The numbers 1 – 9 have been placed in each part of a diagram made with five boxes. The total of the numbers in each box is also shown when you use the applet that can be opened by clicking on the diagram.

Part 1

How can the numbers be placed so that the numbers in all but one box add to a common total? What different common totals can be made?

Part 2

How can the numbers be placed so that the totals in the boxes are all the same?

You could use ‘guess and check’ for this question, but there is another way if you think about the numbers that are used in two boxes and what they have to add to.

 

 
 

Natural Maths : Ph 07 5533 2916 : Fax 07 5533 7244 : nmaths@naturalmaths.com.au