Being resilient

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

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 more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?