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Mission2012
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Maybe I'm misunderstanding something, because I get 156 possible games.
Here's how I figure it:
let's say the couples are AB JK PQ XY.
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fact 1:
there are 24 possible teams.
* list them: AJ AK AP AQ AX AY BJ BK BP BQ BX BY JP JQ JX JY KP KQ KX KY PX PY QX QY.
* combinatorially: 8 choices for the first team member; 6 choices for the second (can't pick the spouse, so not 7).
if you just do 8 x 6, you're double-counting every team, so there are (8 x 6)/2 = 24 teams.
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fact 2:
each of these 24 teams can play any of 13 opposing teams.
i don't see a decent combinatorial way here, so, let's just make a list for the teams that "AJ" could play:
BK BP BQ BX BY KP KQ KX KY PX PY QX QY
there's nothing special about "AJ", so every hypothetical team has 13 possible opposing teams.
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ok, let's combine these facts.
24 x 13 games... but, then, you're double-counting each game. so, there should be (24 x 13)/2 = 12 x 13 = 156 possible matchups.
is this the exact wording of the original?
if so, what does the answer key say?
iiiiiiiiinteresting...
