Math CentralQuandaries & Queries


Question from Jade, a student:
Pat, Joe, Dave,Yoly, Dolor and Alma are three brothers - and sister - pairs who
play double tennis. Brother and sister ca not play in the same pair. Pat and Yoly
play Dave and Dolor on one day. Dave and Yoly play Joe and Alma on another
day. Name each brother - and sister pair, in any order.

One way: make up a table with (say) guys on the rows and gals on the columns. Then put X marks for pairs that you deduce cannot be brother-sister pairs and check marks for ones that are. A pair can be impossible either because they have played together or because you have already determined somebody else to be the brother or sister of one of them. A pair can be shown to be brother and sister if one of them is not anybody else's brother or sister.

This method will be enough for this problem. For harder problems you may have all the information written down and still not be able to deduce a solution directly. In that case fill out what you can in ink and use _pencil_ to add one guess that will let you work out some more. If you get an impossible situation (here, if the chart shows somebody has two siblings or none) you have shown that the guess was wrong; go back and put in the opposite symbol in ink.

Good Hunting!

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