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## 'Fractions in a Box' printed from http://nrich.maths.org/

We have a game which has a number of discs in
seven different colours. These are kept in a flat square
box with a square hole for each disc. There are $10$ holes in each
row and $10$ in each column. So, there would be $100$ discs
altogether, except that there is a square booklet which is kept in
a corner of the box in place of some of the holes.

We haven't drawn a grid to show all the holes because that would
give the answer away!

There is a different number of discs of each of the seven colours.

Half ($\frac{1}{2}$ ) of the discs are red, $\frac{1}{4}$ are
black and $\frac{1}{12}$ are blue.

One complete row (of $10$ holes) of the box is filled with all
the blue and green discs.

One of the shortened rows (that is where the booklet is) is
exactly filled with all the orange discs.

Two of the shortened rows are filled with some of the red discs
and the rest of the red discs exactly fill a number of complete
rows (of $10$) in the box.

There is just one white disc and all the rest are yellow.

How many discs are there altogether?

What fraction of them are orange?

What fraction are green? Yellow? White?