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?
You can use five marks on a ruler of 16 cm.
2  5  5  1  2  1
_ _  _ _ _ _ _  _ _ _ _ _  _  _ _  _
instead of
1  1  3  3  3  3  2
_  _  _ _ _  _ _ _  _ _ _  _ _ _  _ _

Posted by monica
on 20081116 14:33:06 