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Singleton Settlement II (Posted on 2013-07-03) Difficulty: 3 of 5
Doris, Laura, and Renee played two card games in which the objectives were : (a) to form pairs by drawing cards, and (b) to escape being left with a singleton.

The players took turns drawing a card from another player’s hand; drawing continued until one player was left with the singleton. When a pair was formed after a drawing, the pair was discarded

After drawing a card from a second player's hand and discarding a pair, some player would be left with no cards at some point; in that event the third player would draw from the second player's hand when it was her turn to draw.

Near the end of each game:

  1. Doris held just one card, Laura held just two cards and, Renee held just two cards; the combined hands contained two pairs and a singleton, but no one hand contained a pair.
  2. Doris drew a card from Laura's hand and could not form a pair.
  3. Laura was to draw a card from Renee's hand, after which Renee was to draw a card from Doris' hand.
  4. No player was to hold the same hand twice in any one game.
  5. The player who was to be left with the singleton was to be left with it for the first time.
Who escaped being left with the singleton in both games?

No Solution Yet Submitted by K Sengupta    
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answer Comment 1 of 1
(5) is a bit ambiguous, as it does not indicate that it wold apply to each individual game OR both games. 
Assuming that it applies to each individual game, from the givens the same person ended up with the singleton in both games.  Given only three plays, it can be deduced that after Renee drew a card from Doris' there only remained the singleton in Doris' hand, as both Laura and Renee must have formed pairs reducing the hands to a single player holding the singleton, and noting from (1) and (2) that Doris had two cards before Renee's draw. From (4), Doris did not begin with the singleton, and as both Laura and Renee drew pairs. As Doris ended up with the singleton but did not begin with it, Doris must have drawn it from Laura's hand. This leaves Renee not having had the singleton during any of the last three plays of both games. The answer would then be that Renee escaped being left with the singleton in both games.

If (2) and (3) of the numbered givens only indicate the order in which the the players drew cards from each others hands and not the limited sequence of three draws, it is possible for Laura to have ended up with the singleton. But, again from (4), Renee would not have ended up with the singleton.

  Posted by Dej Mar on 2013-07-04 00:28:38
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