# The soldiers

Arturo has plastic dolls shaped like Indians, soldiers, cowboys and horses in identical quantities for each of the four categories. On the day of his birthday he invited some friends to play and at the end of the day he found that he was missing a third of his dolls.

He also verified that:
He has as many horses as cowboys left.
He has two Indians out of three.

How many soldiers were lost?

#### Solution

We know that Arturo has the same number of cowboys, horses, Indians and soldiers. If we call x to each of those amounts, in total it has 4x toys.

When he finishes playing he realizes that he is missing Y jeans and fit Y horses, then you are missing (x-y) horses. We also know that a third of their Indians are missing and we do not know the amount of soldiers that are missing what we call z.

That is, it lacks

As on the other hand they tell us that this amount is one third of the initial number of toys, we can write that:

This is only true if z = 0, that is to say, no soldier is missing.