## 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