Distinct diagonals

Weekly Problem 21 - 2010
How many diagonals can you draw on this square...
Age
11 to 14
Challenge level
filled star empty star empty star
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem



Sixteen unit squares are arranged to form a square array as shown in the diagram.

Distinct Diagonals


What is the maximum number of diagonals that can be drawn in these unit squares so that no two diagonals share a common point (including endpoints)?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.