Being resilient

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

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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?

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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

It would be nice to have a strategy for disentangling any tangled ropes...

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

Can you make sense of these three proofs of Pythagoras' Theorem?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?