Question 1: Not a multiple of 9

How many of the numbers from 1 to 90 can you choose such that no two of your numbers add to a multiple of 9?

Question 2: Paths from 1 to 12

You have to find a way to go from the square labelled 1 to the square labelled 12. You can move in any direction (horizontally, vertically or diagonally) so long as you move into a square where the number is larger than the one you are currently in.

How many different paths are there from 1 to 12?

Question 3: Corner Circles

In this 3 × 3 grid, the circles at the corner of each square have to be coloured either black or white. The number in the centre of each square tells how many of the circles at its corners should be coloured black.

Be a STAR problem solver

Click on the diagram above to start an applet that gives you lots of examples of this problem. You can use this applet to help you Sort out what the question is all about and to Think about a strategy for finding which circles need to be coloured black.

Action and Reflection

Click on the link below to start the applet for a 5 × 5 grid and use two examples of the problem that you solved to explain any strategies that you found helped you solve the problem.