Participants: Book, Candy, Flowers, Money and Scarf.
Gifts: book, candy, flowers, money and scarf.
The participants are unmarried, grown-up people of mixed genders, each being both a giver (donor) and a receiver, in a way that no one gave or received an item bearing his or her name and none gave a present to the person from whom he or she received one.

The present received by Flowers was the name of the donor of the scarf, Scarf sent flowers to the book-giver, Candy gave Scarf a present and Book received candy.

a. Find out, who gave what to whom.
b. You may deduce (with no certainty) from the nature of the gifts the probable gender of each of the people mentioned,

Source : (Slightly abridged) problem #98 from Penguin’s Problems book by William and Savage 1940.

Since nobody gave a present to themself or the person that gave something to them, the only way to do this with 5 people is a 5-cycle. Then, Book gave something to somebody who gave something to somebody who gave something to somebody who gave something to somebody who gave something to Book. We actually only need the clues that Scarf gave flowers to the book-giver and Candy gave Scarf a present. The present that Candy gave Scarf cannot be candy or a scarf. Since Scarf gave flowers to the book-giver, Candy could not have given flowers to Scarf, and Candy cannot be the book-giver because Scarf cannot give something to Candy who gave something to Scarf. Therefore, Candy gave money to Scarf. The book-giver that Scarf gave flowers to cannot be Book or Flowers, so it is Money. Then, Money cannot give a book to Book, so Money gave a book to Flowers. Then, Book gave Candy a present, but it cannot be candy, so it is a scarf. Then, Flowers gave candy to Book. The present received by Flowers was a book, and Book gave a scarf. Therefore, Book gave a scarf to Candy, who gave money to Scarf, who gave flowers to Money, who gave a book to Flowers, who gave candy to Book.

Edited on December 3, 2023, 4:08 pm

Posted by Math Man on 2023-12-03 11:17:44