Being resilient

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you replace the letters with numbers? Is there only one solution in each case?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

How many different triangles can you make on a circular pegboard that has nine pegs?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

There are nasty versions of this dice game but we'll start with the nice ones...

Can you use the information to find out which cards I have used?

Use the information on these cards to draw the shape that is being described.