I have an unmarked ruler (AD) of length 6cm. Making two marks in it, one (B) at 1cm from the left end and other (C) at 2cm from the right end, I´m able to measure any integer length from 1 to 6 cm:

       +----+-------------+--------+
       A    B             C        D

AB = 1cm / CD = 2cm / BC = 3cm / AC = 4cm / BD = 5cm / AD = 6cm.

If I have an unmarked ruler of length 14cm, what is the minimum number of marks, and where do I have to make them, in order to be able to measure any integer length from 1 to 14cm?

I recognized this puzzle as soon as I saw it, but couldn't remember the official name until I searched Mathworld.

http://mathworld.wolfram.com/GolombRuler.html

Posted by Brian Smith on 2008-11-16 00:32:35