Mathematics challenges to end 2023 – 12/26/2023 – Marcelo Viana

It’s time for one of this column’s greatest traditions: our end-of-year math challenges! There is no template: the whole point is having fun looking for solutions, if possible in the company of family and friends. I hope you like it, and I wish you all a Happy New Year!

1. In the foreign languages ​​course, the teacher finds that 17 students speak English, 11 speak Spanish, 7 speak both languages, and 8 speak neither. How many students are there in the class?

two. Florbela, the florist, is upset because the supplier delivered more red roses than white: 5 red for every 4 white. Now, in her famous bouquets, she uses exactly half a dozen of each color. But sales are good: 16 bouquets came out in a single day! Florbela notices that now, among the remaining flowers, there are 3 red roses for every 2 white ones. How many roses of each color had she received from the supplier?

3. Spending time at the market with his grandmother, a fruit seller, Pitanga watches the scales. She notices that an apple weighs the same as two kiwis. An apple and a kiwi together weigh the same as a banana. Two bananas and two kiwis weigh the same as an apple and a pear. How many apples does Pitanga need to place on the scale pan to balance it with a pear on the other pan?

4. Mr.’s room Carré is rectangular, measuring 10.8 m by 5.2 m. He wants to cover the floor with mosaics, but he insists that they are square and that none of them need to be broken. Mosaics can be made to measure: the only restriction is that the side length corresponds to a whole number of centimeters. What is the maximum size of mosaic that you can have? Can Carré use it, and how many do I need to order?

5. Tom Cruise on yet another impossible mission: recovering Taylor Swift’s autographed guitar stolen by a gang. The precious instrument is protected by eight alarms (A1 to A8): if any of them go off, our hero will die and, much worse, the guitar will be lost forever! Fortunately, there are six buttons (B1 to B6) that, each time they are pressed, switch some alarms from “on” to “off” and vice versa. The problem is that each button controls different alarms: B1 controls A1, A3, A5 and A7; B2 controls A2, A3, A6 and A8; B3 controls A1, A4, A5 and A6; B4 controls A2, A4, A6 and A7; B5 controls A1, A2, A5 and A8; and B6 controls A3, A4, A7 and A8. When Tom arrives at the scene, all the alarms are on. What buttons should he press to turn them off? Does order matter?

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