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Building a ruler (Posted on 2008-11-14) Difficulty: 2 of 5
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, Im 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?

See The Solution Submitted by pcbouhid    
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re: Catch? | Comment 5 of 10 |
(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 2008-11-14 23:48:22
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