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Can you get 11 points in rugby?

theguardian.com - Did you solve it? Are you smarter than a rugby commentator? - The Guardian

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Earlier today I asked you three questions about rugby scores

1) What is the highest score that can be made in only one way?

2) What is the highest score that can be made in at most two ways?

3) What is the highest score that can be made in at most three ways?

Rugby scores are either 3 (a kick), 5 (a try) or 7 (a try and conversion).

The solution

There is no pretty way to solve this out. We need to count up from the lowest possible scores and see how these scores are made:

1 - impossible score

2 - impossible score

3 - one way (kick)

4 - impossible score

5 - one way (try)

6 - one way (2 kicks)

7 - one way (try and conversion)

8 - one way (try and kick)

9 - one way (3 kicks)

10 - two ways (2 tries OR try, conversion and kick)

11 - one way (try and 2 kicks)

12 - two ways (try, try and conversion OR four kicks)

13 - two ways (try and conversion and 2 kicks OR 2 tries and a kick) 14 - two ways (2 tries and 2 conversions OR 3 kicks and a try) Now we have the answer to the first question. The numbers 12, 13 and 14 are three numbers in a row that can be made in two ways, so we can deduce that every subsequent number can be deduced in at least two ways. This is because: 12 plus a number of kicks gives us 12, 15, 18, 21, 24,... 13 plus a number of kicks gives us 13, 16, 19, 22, 25,... 14 plus a number of kicks gives us 14, 17, 20, 23, 26...

which covers all the numbers.

So, 11 is the highest score that can be made in only one way. The second and third questions can all be solved using the same method. 16 is the highest score that can be made in at most two ways. 19 is the highest score that can be made in at most three ways. In fact, if you want to carry on working out the highest score that can be made in at most n ways, you get: 11, 16, 19, 23, 26, 29, 32, 34, 37, 39, 41, 44, 46, 47, 49, 51, 53, 54, 56, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 74, 76, 77, 79, 79, 81, 82, 83, 84, 86, 86, 88, 89, 89, 91, 92, 93, 94,... 94 is the highest score that can be made in at most 49 ways. This sequence is now registered in the Online Encyclopedia of Integer Sequences, listed A261155. Which means that this puzzle column has finally produced a mathematical result of note! Hopefully it will be the first of many... Thanks to Matthew Scroggs of Chalkdust Magazine for this puzzle, and for submitting the sequence to the OEIS. 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.

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What's the hardest position in rugby?

For their part, props occupy the toughest and most punishing position in rugby and take a lot of hits during the course of a match. Whether you're a hooker or a prop, going in for physical contact is all part of your job, which requires a lot of physical strength.

offload-rugby.co.uk - WHO PLAYS WHERE IN A RUGBY UNION TEAM: THE POSITIONS

The front row

You've no doubt heard of a prop or a hooker. These are the players that make up the front row. There are three of them - two props, wearing numbers 1 and 3, and a hooker, wearing number 2 - and they are the first players to come into contact with the opposition. Their basic role is to push at scrums and to clear out rucks. Stocky and not very tall, they get themselves noticed because they are often at the heart of the action. They are the first line of defence but also have a role to play in helping their team move forward. But why are there two props and one hooker? And what is the difference between the two positions? The simple explanation is that the two props are positioned on either side of the hooker, who, being lighter on their feet and quicker, must drive holes in the opposition defence and help their side move forward. Hookers need to be brave in playing a central role in the scrums, and they need to have blind faith in their two props. For their part, props occupy the toughest and most punishing position in rugby and take a lot of hits during the course of a match. Whether you're a hooker or a prop, going in for physical contact is all part of your job, which requires a lot of physical strength. Playing at hooker involves using your speed more. But if you're all about brute strength, then there's no doubt you should be pulling on the No. 1 or No. 3 jersey.

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