Being resilient

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?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Explore the effect of combining enlargements.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Sequences of multiples keep cropping up...

The number in the square is the mean of the four numbers surrounding it. Can you find the missing numbers? 

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

The clues for this Sudoku are the product of the numbers in adjacent squares.