mathschallenge.net logo

Perfect Ruler

Problem

By marking off six unit lengths on a piece of wood, we can make a ruler to measure all the lengths from 1 to 6 units directly.


But it is possible to achieve the same thing by using just two marks.


What is the minimum number of marks necessary to measure all the lengths from 1 to 12 units?


Solution

The minimum number of marks is 4 and three different solutions are given.


Some logic can be applied to solve the problem:
Where must you place a mark in order to measure 11?
What do you need to do now to measure 10?
And so on...

How many different solutions for a length 12 ruler exist?
What is the shortest ruler that requires 3 marks?
Investigate different length rulers.

Problem ID: 70 (Mar 2002)     Difficulty: 2 Star

Only Show Problem