Four Trees Puzzle
A lateral thinking problem where the assumption of a flat plane prevents finding a solution to plant four trees equidistantly; the answer requires placing one tree on a hill (or in a hole) to form a regular tetrahedron.
THE IDEA
Problem
A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How would you arrange the trees?
The usual procedure is to try and arrange four dots on a piece of paper so that each dot is equidistant from every other dot. This turns out to be impossible. The problem seems impossible to solve.
The assumption is that the trees are all planted on a level piece of ground. If one challenges this assumption one finds that the trees can indeed be planted in the manner specified. But one tree is planted at the top of a hill and the other three are planted on the sides of the hill. This makes them all equidistant from one another (in fact they are at the angles of a regular tetrahedron). One can also solve the problem by placing one tree at the bottom of a hole and the others around the edge of the hole.
When to use it
When stuck on a problem, write down every assumption and challenge each one.
In design thinking sessions, use the 'four trees puzzle' as an icebreaker to encourage lateral thinking.
In mathematics education, demonstrate that extending a problem from two dimensions to three can unlock new solutions.
In strategic planning, question industry norms and assumptions to discover innovative approaches.
FROM THEORY TO EVERYDAY LIFE
In practice
Planting Four Trees
A gardener must plant four trees so each is the same distance from every other. Attempting to place them on flat ground fails. The solution involves raising one tree on a hill or lowering it in a hole, forming a regular tetrahedron.
Real-World Analogy
In a team project, members assume all work must be done sequentially. By challenging that assumption, they find parallel workflows that achieve the same goals faster.
A MOMENT TO REFLECT
Put it to work.
What hidden assumptions did you automatically make when first presented with the tree-planting problem?
Can you think of a personal or professional situation where challenging a basic assumption led to a breakthrough?
How might you deliberately list and test assumptions in your next complex problem?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Lateral Thinking A Textbook of Creativity (Edward de Bono)