159928

Firstly, we know what the purple square is because it is x cubed and because the shapes each stand for a number between 0 and 12 there is only one possibility, 2. It cannot be 1, because 1 cubed is 1 and the answer to the sum is a different shape. It cannot be 3 because 3 cubed is 27 seven and 27 is greater than 12. By working out what number the square represents we can work out that the semi-circle is 8 (2 cubed/ 2x2x2). We can work out the oval because the sum shows the square- which we know is 2 times the oval equals the semi circle- which we know is 8. Then we do 8 divided by 2 which equals 4 to find out the value of the oval. Next we can work out the circle. There are two sums which can help us do this. The rectangle times the oval (4)= circle and the triangle times the square (2)= the circle. We know that the value of the circle must be a factor of 4 and 2 and the only three numbers are 4, 8 and 12. 4 is the value of the oval and 8 is the value of the semi-circle so the red circle must be 12. From this, we can work out that the rectangle is 3 (12- circle divided by 4- oval) and the green triangle is 6 (12- circle divided by 2- square). We can work out what the eight pointed star is because there is a sum showing the rectangle (3) times the rectangle (3) which equals 9. Next we can work out the diamond. The rectangle (3) times the diamond equals the rectangle (3). To find out the diamond we do 3 divided by 3 which equals 1. We can check this with diamond (1) time hexagon = hexagon. This makes sense because one multiplied by any number (not zero) will be the number you multiplied by one. We can also work out the red triangle. The square (2) multiplied by the red triangle equals the red triangle and the red triangle multiplied by the semi-circle (8) = the red triangle. The only possible value of the red triangle is zero, because anything multiplied by zero equals zero. Now we only need to find out two more shapes, the purple star and the hexagon. The only sum which will help us is the square (2) multiplied by the purple star equals the hexagon. There isn't a way to work it out mathematically so we must see what we already know to work out what the value of the two shapes are. So far, we know...
Square=2
Semi-circle=8
Oval=4
Rectangle=3
Circle=12
Green Triangle=6
8 Pointed Star=9
Diamond=1
Red Triangle=0
The only three numbers from 0-12 which aren't in the list are 5,7 and 10.
The sum is square (2) multiplied by the purple star equals the hexagon. The only numbers which make sense in the sentence are 5 and 10. Therefore, the purple star must equal 5 and the hexagon must equal 10