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The Stable Roommates Problem matches 2n participants into n sets of roommates based off of each participant's list of preferences. I was wondering if there was a variant of this problem where the number of roommates is different. For example, matching 10n participants into n sets. Thanks for the help.

Edit: The Hospital Resident problem is also similar to this. Each hospital can take a certain number of residents. The problem is the residents list their preferences by hospital instead of other residents.

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    $\begingroup$ I'm not sure a stable assignment (properly defined) exists in this setting – have you considered that? $\endgroup$ – Yuval Filmus Mar 8 '14 at 5:39
  • $\begingroup$ I'd also be interested in knowing if there isn't a solution. $\endgroup$ – Connor Mar 8 '14 at 6:07

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