Ten trees must occupy twenty places across five rows. The escape is to let every tree work for two lines at once.
Five Rows
Riddle statement
You want to plant 10 trees.
Arrange them so that they form five distinct straight rows, with exactly four trees in each row.
A tree may belong to more than one row.
How would you arrange them?
Show solution
Solution
Draw a pentagram and place one tree at each of its ten distinguished points:
- the five outer vertices;
- the five inner intersection points.
Each of the star's five main straight strokes contains exactly four trees:
- two outer vertices;
- two inner intersections.
This gives five distinct straight rows of four trees each.
The total number of row memberships is:
5 rows × 4 trees = 20.
This is possible because each of the ten trees belongs to exactly two of the five rows:
10 trees × 2 rows = 20.
In this arrangement, the only lines containing four trees are precisely the five main strokes of the pentagram.