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### Number and algebra

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# Mathdoku

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Age 7 to 11

Challenge Level

The idea of this task is to complete the four by four grid so that the numbers 1, 2, 3 and 4 appear only once in each row and only once in each column.

You will see that some squares, or groups of squares, are outlined with a thick black line. These groups of squares are called 'cages'.

In the corner of one of the squares in a cage, you will see a small target number and usually a mathematical operation too. For example, if a cage of three squares has '8x' in the corner of one of the squares, it means that the three numbers in that cage multiply together to make 8.

If the cage is made up of only one square, which has a number in its corner but not an operation, that number is telling you exactly what goes in that square.

Have a go at the grid in the interactivity below. Clicking on a square allows you to type in a number, or choose a number from the options given. You can change your mind just by typing/choosing another number instead.

**How would you convince someone else that the number you have put in a square must be correct?**

Click on the Settings menu (the purple cog in the top right-hand corner) to select another grid to try. You can increase the level of difficulty in the Settings menu too.

If you would prefer to work away from the computer, you can print out these grids: Mathdoku grids of difficulty 1, Mathdoku grids of difficulty 2, Mathdoku grids of difficulty 3.

You may also like to take a look at the mathematical Sudokus feature, which includes also 3 by 3, 5 by 5 and 6 by 6 Mathdokus.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?