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Byline: with Steve Humble

Dear Dr Maths, For homework my daughter has been trying to find the largest number of non-overlapping triangles that can be created by drawing a set of straight lines.

We have managed to find seven triangles with six lines but then get a bit stuck ... can you help? Richard (Dad in need of maths help!), via email.

The reason that you get stuck is that this is a tricky maths problem to solve and the general answer for all possible triangles has not yet been found for any more than 11 lines.

Called The Kobon Triangle Puzzle, it is named after the Japanese puzzle expert Kobon Fujimura.

With three lines the most you can make is one triangle. With four lines you can create two triangles; five lines result in five triangles and six lines give seven triangles.

If you continue to draw new lines, the puzzle becomes more and more complex to find the maximum number of possible triangles you can create.

As illustrated in the pictures below.

You also create some fantastic triangular doodles!

You can use the idea of Kobon triangles to create mathematical art, colouring the triangular regions to form different patterns.

The general formula for how many triangles you get, given any number of lines, is not known. Here are some of the known results: Number of lines 34567 8 910 Maximum number of triangles 1 2 5 7 1115 21 Here is a puzzle for you to try: Above shows one way of drawing two triangles with four lines. How else can you draw four lines and get two triangles? The first correct entry drawn will win Dr Maths' new book Code Breaker Explorer available from all good book shops or see for more information.

The answer to last fortnight's quiz was the next three Lucky Numbers after 99 are 105, 111, 115.

Do you have a maths question or problem? Write to Dr Maths, Evening Chronicle, Groat Market, Newcastle, NE1 1ED or send an email to
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2012 Gale, Cengage Learning. All rights reserved.

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Publication:Evening Chronicle (Newcastle, England)
Date:Nov 15, 2012
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