We're looking for a treasure Here's a problem my sister-in-law just sent me and she doesn't find the answer. It's to help her daughter.
We have a map of an island. On this island there's a palm tree P, a house M and a big rock R. The rock is 8 meters far from the palm tree, and 5 meters far from the house. The house is 4 meters far from the palm tree. And we know that:


*

*the treasure  is < 6 meters from the palm tree

*the treasure  is > 4 meters from the house

*the treasure  is < 5 meters from the rock


On the island below put points M and P using the previous clues.
Color the zone where we have to dig to be sure to find the treasure.

Could you explain the basic principles of how to solve that problem/draw what's asked (the picture is not the actual one)?

My answer is not much different than what @Nick, who was quicker, already posted. But here it is, there is one detail at the end that is a bit different. 
See the picture below. Start with a circle centered at the rock, R, with radius $8$, I have labeled this circle 8R, meaning "8 from the rock". Pick a point P on that circle, and call it the palm. The house is on the circle 4P and also on 5R, these two circles intersect at two points, just pick one of them to be the house H. The treasure is inside <6P, outside >4H,and inside <5R, so it looks like a triangular area on the picture. 
But, given we do not know which direction is North, etc, and which direction the palm is from the rock, etc, we have only determined how far away from the rock the treasure could be. If the palm was at a different direction from the rock, then that triangular area would end up in a different direction too, although certainly same distance from the rock. So it could be anywhere in the area sprinkled with blue on the picture, outside the green circle and inside the <5R circle. 

