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)
As you pointed out it's easy to see there's more than one solution, thus rather than focusing on "the" solution, a solver might provide one such solution.
However, I think the main point is to prove you can't do it with 4 or fewer marks, since there's theoretically 15 distances. (Also keep in mind this is D2, so it's unlikely the solution is anything difficult)

Posted by Gamer
on 20081114 18:33:08 