# Distinct Diagonals

Weekly Problem 21 - 2010

How many diagonals can you draw on this square...

How many diagonals can you draw on this square...

## Problem

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

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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.

## Student Solutions

The most you can get is $10$, eg:

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