Opinion – Marcelo Viana: Mathematical challenges for the family on New Year’s Eve

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On January 2, 2021, Mr. Amilton wrote to me: “I read the column ‘mathematical challenges’ and sent it to my children. My daughter called from Belgium to discuss the results, very excited. On the 1st, I had lunch with the in-laws of my son. It was very good and the most enjoyable subject was the resolution of challenges”. The daughter, Paula, corroborated.

Imagining the family getting together to have fun with math is very rewarding. Hopefully this year’s challenges repeat some of that magic. Responses are welcome by email: [email protected].

1. John picks up his socks in the dark so as not to wake his wife, but the drawer is a mess, with the socks all sorted and mixed up. He remembers that he has 53 socks: 21 blue, 15 black and 17 red. How many does he need to get to make sure he’s selected some pair of black socks?

2. The birthdays of Abel, Bela, Ceci, Davi and Elza fall on consecutive days, from Monday to Friday. Ceci is two days older than David. Abel’s birthday is as many days before Elza’s as Bela’s birthday is after David’s. Elza’s birthday is on Thursday. When is each child’s birthday?

3. Mary has three identical boxes: one contains two white balls, one contains two black balls, and the other contains a white and a black ball. She chooses a box at random and, without looking, takes out one of the balls. Knowing that this ball is white, what is the probability that the other ball in this box is also white?

4. Artur and Bento want to know when Carla’s birthday is. It lists ten possible dates: May 15th, 16th or 19th, June 17th or 18th, July 14th or 16th, and August 14th, 15th or 17th. Then, separately, he tells Artur what the month is and Bento what the day is. Artur says: “I don’t know the date, but I know that Bento doesn’t know either”. Bento replies: “I didn’t know, but now I do.” “So I know too,” exclaims Arthur. When is Carla’s birthday?

5. Ana, Bia and Céu play successive Ping-Pong matches: whoever wins keeps playing, whoever loses gives way to whoever is sitting. In the end, Bia is exhausted because she played straight through the last seven. In total, she played 12 games, Céu played 14 and Ana only 8. Who won the fourth game, and from whom?

Happy New Year, with lots of joy and math to everyone!

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