July 15, 2024

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# Obmep: A logical question about flowers that sparks curiosity and spreads quickly – 06/05/2024 – Science

A question about flowers at the first stage of the 19th Brazilian Mathematics Olympiad for Public Schools, held on Tuesday (4), aroused curiosity – and even a little anger and insult.

In the test, which the Institute of Pure and Applied Mathematics has held annually since 2005, one of the questions showed a picture of five yellow and purple flowers and told the story of Anna, Pia and Carla, who went to a flower shop and there learned that each one of them would be given one of these flowers.

Below are the flowers that can be given as a gift.

See the rest of the question:

Anna, Pia, and Carla visit the flower shop in their neighborhood. The seller separated the five flowers shown in the picture and said he would give each person one of these flowers.

Carla overheard the following conversation between Pia and Anna:

– “Hi Anna,” Bea said, “Carla and I know the color of each flower we will receive, but neither she nor I know how many petals each of us will receive.”

“I know how many petals I’ll get, but I don’t know what color they are,” Anna said.

From this conversation, Carla finds out which flower Anna will win. What is this flower?

For you, which flower will Anna win?

Below, with the help of Pedro Malagotti, a member of the Obmep exam panel, we explain how you can solve this question, which involves only text interpretation and reasoning.

1. We know from the statement that each person will win one of the five flowers on offer.

2. Two flowers have the same number of petals (three) but different color

3. On first reading, Anna’s speech is the only one that provides salient information: She knows the number of petalsbut not the color

4. With this information about Anna, it is possible to understand that this suspicion is only possible If Anna receives the three-petaled flower (As seen in step 2)

5. Now we know that Anna will get a three-petaled flower

6. Returning to reading the statement, we see that Carla is listening to everything and that she hears Bea saying that they know the colors of the flowers they will have, but they do not know how many petals they will have; Then listen to Anna’s speech

7. Thanks to the information you hear from Anna, you will be able to find out which flower Anna will win. So we know it has certainly Which flower is it?

8. Certainty can only occur in one scenario: if Carla and Pia both receive purple flowers, given that one of the purple flowers will also have three petals

9. In this way, Anna’s flower can only be Three yellow petals

This is because in other scenarios – if Carla and Pia had yellow flowers or each received one of a different color – it would not be possible to be sure which flower Anna would receive.

The only scenario that brings certainty to Carla’s conclusion is if she and Pia receive the two available purple flowers, which would necessarily result in Anna receiving the three-petaled yellow flower—because the other three-petaled flower would be either Carla’s or Pia’s.

“In the end, you know exactly what happened to Ana. But you’re not sure what happened to Pia and Carla,” Malaguti says.