The Perfect Golomb Ruler
In The Murderous Maths of Everything we see a PERFECT Golomb Ruler.
This ruler only has four marks but it can measure any distance between 1 and 6 units. Most importantly, it can only measure each distance in ONE way. It is impossible to make a perfect Golomb ruler longer than this.
Longer Rulers
Although you can't make a perfect ruler longer than 6 units, the big challenge is to choose how many marks you want to use, then you see what is the shortest ruler you can put them on so that you can’t measure the same distance in two different ways.
This 11 unit ruler has five marks. It has only one way to measure any length of 1,2,3,4,5,7,8,9,10 or 11. It would be perfect apart from the sad fact that you can’t measure 6! If you try to put 5 marks on a ruler measuring 10 units or less, then you’ll find you can measure at least one length in two different ways which breaks the rules of the ruler. This 11 unit ruler is the shortest you can put five marks on so it’s called the optimal Golomb ruler for order 5.
At the moment computers are trying to find the shortest ruler you can put 25 marks on.
They are checking this green one to make sure that there's no way to measure any distance twice. This ruler was invented back in 1984, and it’s 480 units long! Go on, join in, you know you want to. Can you find any distance that can be measured in two ways?
Or better still, if you want to be famous for ever can you design a shorter ruler with 25 marks on that works?
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