To prepare for this week’s World Cup, here’s the rugby points puzzle. Think you’ve solved it? The solution is here

Can you solve it? Are you smarter than a rugby commentator?

Hello guzzlers,

The Rugby World Cup kicks off this Friday. So here’s a puzzle that could come in handy over the next few weeks, especially if you are a rugby commentator.

As any rugby fan will know, a frustrating aspect of the sport is that when you see a score it is not always clear what has been scored.

This situation is down to the points system:

3 points for a penalty kick or drop goal



5 points for a try



7 points for a try and a conversion

For example, if a team has 21 points, this could be three tries and three conversions. Or seven penalty kicks.



Here’s the question:

1) What is the highest rugby score that can be made with only one possible combination of penalties, tries and conversions?

In other words, if a team scores this amount you know exactly the breakdown of what was scored. And if they score any higher, you don’t.

And two more questions for fun:

2) What is the highest rugby score that can be made in at most two combinations of penalties, tries and conversions?

3) What is the highest rugby score that can be made in at most three combinations of penalties, tries and conversions?

And a bonus question, if you thought those were too easy.

What is the highest rugby score that can be made in at most 49 ways?

I’l be back later with the solutions.

Thanks to Matthew Scroggs of Chalkdust Magazine for this puzzle. Matt’s personal website is here.

I post a puzzle here on a Monday every two weeks. I also blog about maths for the Guardian. I’m on Twitter, Facebook, Google+ and here’s my personal website.



If you know of any great puzzles that you would like me to set here, get in touch.

And finally...On Monday 9 November, I’ll be giving a two hour evening class, Exploring the beauty of numbers and patterns, as part of the Guardian Masterclasses Back To School series. You can book here.