The Eastman family has some Christmas present trouble. The trouble isn't buying them in time - they did that well before the time was up. The problem is that the sticky labels they put on the presents to show who was to receive them, and from whom they were, have fallen off. I guess they were old. Anyway. A trait that runs in this family is that they have rather bad memories... bad enough, that they're not even certain which presents they bought. The family consists of Alice, her husband Bruno, their older child Deirdre and her younger brother Chester. Each person gave one gift to each of the other members of the family. Their memories are not uniformly bad. In fact, one of them is always correct, and another is correct three-quarters of the time. The third is right half of the time, and the last one is right one-quarter of the time. I'm not going to tell you which is which, though. That would make this puzzle too easy.

The following are pieces of discussions among the family after they opened the presents and tried to figure out their ownership status:

Alice: "Well, this is a mess. I'm pretty sure the watercolours belong to Chester, though." Deirdre:"The DVD player is mine." Bruno:"I thought the DVD player belonged to Alice." Deirdre: "The textbook on differential equations and the silk ribbon both belong to mom." Bruno:"No, the textbook is Chester's." Chester:"And the pocket watch is yours, right?" Bruno:"The diary and the box of chocolates are mine." Chester:"And the silk ribbon, too." Bruno:"I gave the model train." Chester:"And the DVD player came from me." Alice:"I do believe the ribbon is mine." Deirdre:"The loudspeakers are yours, though, dad." Bruno:"I got the mittens from Alice." Chester:"I'm the one who gave the silk ribbon." Alice:"The model train was given by Deirdre..." Deirdre:"The socks belong to mom." Alice:"I gave the diary." Deirdre:"And the pocket watch is Chester's." Alice:"The diary and the pocket watch belong to Deirdre." Chester:"The diary is from me." Bruno:"I gave the DVD player, didn't I? I think so." Chester:"I gave the textbook." Alice:"I think the loudspeakers were a gift to Bruno from Chester." Deirdre:"The model train is dad's." Chester:"And mom gave the pocket watch." Deirdre:"The chocolates are Chester's." Bruno:"I seem to recall Alice was the one who gave the box of chocolates." Bruno:"Hmm. I gave the socks, I do know that." Alice:"The textbook came from Bruno." Deirdre: "I gave the watercolours to Chester." Chester:"And in return, I gave you the pocket knife." Alice:"I don't think you gave the pocket knife."

So, can you figure out what belongs to whom? Or, more specifically, who gave the pocket knife, and to whom?

Outline How would you solve this problem Tell us how you tried to solve the problem, and what method might have been more successful.The steps involved in reaching your solution are equally, if not more important than the solution itself. Be sure to refer back to the information in thetextbook.

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