Working systematically

The sum of each column and row in this grid give the totals as shown. What number goes in the starred square?

Two sudokus in one. Challenge yourself to make the necessary connections.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Can you find a number and its double using the digits $1$ to $9$ only once each?

If you had 36 cubes, what different cuboids could you make?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column