Nothing is on the Level…NOTHING!
A puzzle about planting trees
Your mission today is to design an arrangement of trees on a desert island, like the one below.
When there is a single tree, no matter where you stand on the island you will always be able to see exactly one tree.
With two trees, however, there are some places where you can see two trees, and there are some places where you can see only a single tree, since the other one is blocked from view.
(For the purposes of this puzzle the island is empty apart from the trees, and a tree is hidden only when it lies directly behind another tree from the perspective of the observer).
The island has 5 trees positioned at the vertices of a regular pentagon, as below. Is it possible for you and two friends to stand on the island, so that the three of you can each see a different number of trees?
What is the highest possible number of people that can stand on the island, with each person seeing a different number of trees, when the island has 6 trees ? Design such an arrangement of trees.
Todays puzzle was written by Daniel Griller, a teacher and puzzle designer whose book of maths problems, Elastic Numbers, is highly recommended.
Ill be back at 5pm with the solutions
I set a puzzle here every two weeks on a Monday. Send me your email if you want me to alert you each time I post a new one. Im always on the look-out for great puzzles. If you would like to suggest one, email me.
My puzzle book Can You Solve My Problems? is just out in paperback.
Read more: https://www.theguardian.com/science/2017/jul/31/can-you-solve-it-are-you-smarter-than-a-forester