# Sunday Times Teaser 2642 – New World Order

*by H Bradley and C Higgins*

A text book with pages 1 to 500 inclusive has three sections, Arithmetic, Algebra and Geometry, each starting on a new page.

The sum of the page numbers in the Algebra section is double the same sum for the Geometry section and the latter is over twice as long as the Arithmetic section.

How many pages are there in the Arithmetic section?

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Here is a straightforward solution:

and here is another solution based on further analysis leading to a Pell equation (see here):

Nice analysis. The following program covers the full solution space.