## Mathematical challenges until the end of 2020 – 12/30/2020 – Marcelo Viana

This is the 200th edition of this column and the last in 2020. The magic of these numbers made me think we all deserve some fun after this surreal year. With a New Year’s Eve party out of the question, I decided to offer readers some math challenges that they can solve as a family. Hope you have fun and I am looking forward to emailing the solutions to [email protected]

1. There are three doors in an auditorium program, and one of them has a car behind it. If the dear reader gets it right, take the big one home with you. Each port has a hint: port 1 says “it’s here”, 2 says “it’s not here”, and 3 says “it’s not on port 1”. The problem is that only one of the tips is true “… where is the car?

2. The King of Afar likes his daughters so much that he has decided that it is better for the kingdom to have more wives than men. Then you decide that all couples should continue to have children until a girl is born. But worried about overpopulation, he notes that every couple stops breeding once they have a daughter. The birth probabilities for both sexes are the same. Will the king achieve the goal? What will be the percentage of women in Bem Longe under these laws?

3. The lucky reader inherits five chains from Great Aunt Joana, each made of four solid gold links. It soon occurs to him that they would make a beautiful necklace together to give to his wife. The goldsmith charges R \$ 100 for each connection that must be broken to make the intersection. How much does the job cost?

4. Carioca Joãozinho is the grandmother of the two grandmothers. The problem is that they live in other states. To resolve the dispute, he suggests the following: every weekend, he randomly drives to the bus station and takes the first bus. If you go to Minas you will visit Grandma Maria; If you go to São Paulo, Grandma Vera. The buses run punctually every 20 minutes in both directions. But after a while, Grandma Maria complains that she only sees her grandchildren in one weekend in five. What’s happening?

5. Madalena prepares a game for her children Amanda, Bernardo and Carolina. Tape a positive number on each forehead and warn that the three numbers are different and that one of them is the sum of the others. Ask Amanda what number she has. This note that Bernardo is 20 and Carolina is 30 and replies “I don’t know”. Bernardo thinks and reacts the same as Carolina. Madalena provokes: “I won from you!”. But Amanda exclaims: “Wait, now I know my number!” What is it and how did she find out?

May the new year come full of health and joy for everyone!

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