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Question: The island of Tikong has seventeen villages and the rugby board needs to select a squad to be sent to the regional Oceania tournament to be held in Savulevu. What is the smallest size of the squad guaranteeing that every village has a player of their own selected? Explain your answer.

My Answer: smallest size equal to $K=$number of boxes$=17$ $r=$number of objects$=17$ players squad guaranteeing that every village has a player of their own selected $N=$minimum number

$N=k(r-1)+1$, $N=17(17-1)+1=273=$ smallest size.

I'm I getting this correct or going astray?

Laurent Duval
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Surdz
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    Is this clear? I think you need to describe the way the squad is selected. How many are on a squad? (if there are $15$ then at least two of the villages will not be represented). What stops the board from selecting the entire squad from one village? For that matter, what stops them from importing all the players from the neighboring islands? More detail is required. – lulu May 31 '16 at 10:56
  • What is the mechanism by which a squad is created? Presumably you mean something like "each village sends $X$ candidates and the squad must be comprised out of these." But I'm just guessing and of course I don't know what $X$ might be. – lulu May 31 '16 at 11:08
  • I suspect that your knowledge of rugby led you to conclude that a rugby squad has just $15$ players. However, the person who posed the question is assuming that the squad will be large enough that each of the $17$ villages is represented on the squad. What does that imply about the size of the squad? – N. F. Taussig May 31 '16 at 11:08
  • The question and answer had been edited, so comments from now on should be about the edited version above. – Surdz May 31 '16 at 13:42
  • I find that question to still be rather confusing, but I'm guessing what you mean is this: "The island of Tikong has $17$ villages with each $17$ rugby players. The rugby board of Tikong has to send a squad of $N$ rugby players to the regional tournament. What is the smallest value of $N$ such that the squad must have at least one player from each village?" If that's what you're asking, your solution is correct. – sTertooy May 31 '16 at 15:04
  • Note that Steamy's comment contains one piece of information that your question does not: that each village has 17 rugby players. Your solution assumes this is true, but it is not written anywhere in the question. – Eric Stucky May 31 '16 at 15:05
  • Can the smallest size be only 17 because 17 is smallest size, since 273 is quite big.... – Surdz Jun 01 '16 at 23:55

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