Question 1

Question 2

Counters are placed in the circles of this star.

1. How many counters do you need to be able to place 2 counters on each side of the star?

2. In what different ways can you arrange the counters so that there are always 2 counters along each side of the star.

Question 3

We placed the numbers 1 - 9 in the row of empty squares at the top of the Neighbour Totals Game Board and looked for interesting patterns in the neighbour totals. What's a neighbour total? It's the sum of two numbers that are next to each other on the game board.

Click on the Game Board to launch an applet that will make the Game Board come to life. When you click on a number you can click in another part of the board to move the number to that place. Use <Alt><Print Screen> to capture a picture of the Game Board that you can paste into your solution document.

Part 1
What is the pattern that you get in the neighbour totals when the numbers 1 - 9 are placed on the Gameboard in order?

Part 2
Can you find a way to make the neighbour totals equal to either 9 or 11?

Suggestion: Try the number 9 in the first square and see how you go from there. You should find four totals that equal 9 and four that equal 11.

Part 3
You'll have noticed that there are 8 possible neighbour totals. What different ways can you find to make the neighbour totals equal to the eight numbers 7, 8, 9, 10, 11, 12, 13 and 14?

Suggestion: The first and last numbers have to add to 6 for this to work, and we mean have to!