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?
(In reply to
Catch? by ed bottemiller)
Though Charlie's analysis is probably the correct and sought after by the poser, there could be a trick solution by interpreting the 14 cm ruler as an additional ruler:
3 marks; a 1 cm mark from one edge and a 4 cm mark from the other edge of the 14 cm and a 2 cm mark from one edge of the 6 cm ruler. Using the combination of rulers and their marks, all integer lengths from 1 cm to 14 cm can be measured.

Posted by Dej Mar
on 20081114 23:48:22 