Question 3
We placed the numbers 1 - 9 in the grid of empty squares on the left 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
How should the numbers 1 – 9 be positioned on the Game Board to make all the neighbour totals different from each other?
Suggestion: Start with the numbers in order (left to right and top to bottom) and see what changes you need to make in order to make all the neighbour totals different. When you have finished, the only numbers in the neighbour totals grid should be 1s.
Part 2
Think of the centre square for a moment and you will see that it has four neighbours (above, below, left and right). Since each of these neighbour positions will hold different numbers, there have to be at least four neighbour totals that are different.
What different ways can you find of arranging the numbers 1 – 9 on the Game Board to make exactly four different neighbour totals?
We
have placed 8 counters (4 light and 4 dark) on this grid. We were hoping
to find that there would be one of each colour in every horizontal,
vertical and diagonal line of four.