Wales scored 38 points in this game against Italy. A converted try is worth 7 points, a try 5 points and a penalty (or drop goal) 3 points. All prime numbers! List the possible ways Wales scored their points.
In fact, there's an interesting investigation here if you start from the lowest score and list the possible ways of scoring it. What is the lowest rugby score that can be scored in 2 ways? 3 ways? and so in. There are some surprising results. What is so special about 38 points?
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There are 3 ways of scoring in rugby - a try, a conversion or a penalty. The result of this game was Wales Women 15 Italy Women 22. Given that Wales scored 2 tries, one conversion and one penalty, and Italy scored 4 tries and a conversion, form two simultaneous equations in 3 unknowns. The number of points for each way of scoring must be a positive integer. Find the possible scoring systems (there is more than one!).
This would be a good trial and error problem for younger students, link to intersection of planes for older kids. |
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