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Programming Enigma Puzzles

20 December 2011

Posted by on **From New Scientist #2788, 27th November 2010** [link]

To design a book of road maps the publisher took a huge square map of the total area covered. He then drew some vertical lines right down the map and some horizontal lines right across the map, thus dividing it into between 50 and 150 identical rectangles. Each rectangle was a whole number of inches wide and a whole number of inches deep. He then cut along the lines and used the small rectangles as the pages of a book.

On buying a copy of the book I was disgruntled to find that, more often than not, a route that I wanted was near the edge of a page. In fact, taking “near the edge” to mean “two inches or less from an edge”, over half of each page was near the edge. This would not have been the case for a page which was 1 inch longer in either direction.

What was the size of each page?

[enigma1623]

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The following Python code runs in 34ms.

Solution:Each page is 12″ x 15″.