Aniversário de Cheryl | Desafios | Matemática | Khan Academy

Summary

In this engaging logical reasoning puzzle, Alberto and Bernardo must deduce the date of Carla's birthday from a list of possible dates. Carla gives Alberto the month and Bernardo the day. Through a series of statements, both logically eliminate possibilities, starting with Alberto's assertion that he knows Bernardo also doesn't know the birthday, leading to the exclusion of May and June. After further reasoning, Bernardo figures out the birthday, and Alberto, based on this information, concludes the exact date. The puzzle culminates in the discovery that Carla's birthday is on July 16th, showcasing the power of logical deduction.

Takeaways

• 😀 The puzzle involves Alberto and Bernardo trying to deduce Carla's birthday based on a list of possible dates and some clues.
• 😀 Carla provides Alberto with the month of her birthday and Bernardo with the day, allowing them to work together logically to figure it out.
• 😀 Alberto's first statement is that he doesn't know the birthday, but he is sure that Bernardo also doesn't know it, which excludes certain months.
• 😀 After hearing Alberto, Bernardo realizes the exact date. This implies that the day he knows appears only once in the remaining possible dates.
• 😀 Alberto, after hearing Bernardo, concludes the exact birthday. This is only possible if he has the month with a single remaining option.
• 😀 The initial list of possible dates includes May, June, July, and August with multiple days for each month.
• 😀 The logic behind the puzzle relies on eliminating dates based on what each person knows and their subsequent statements.
• 😀 Alberto’s certainty that Bernardo doesn’t know the date means the month cannot be May or June because they each have unique days (May 19 and June 18).
• 😀 After Alberto's deduction, the remaining possible dates are narrowed down to July and August, leaving out May and June.
• 😀 Bernardo's ability to deduce the exact birthday means he received a day that only appears in one of the remaining months. This excludes July 14 and August 14.
• 😀 The final deduction from Alberto is that the birthday must be July 16 because if it were August, he would still be uncertain between two options.

Q & A

What is the primary logic puzzle presented in the transcript?

The primary puzzle involves two people, Alberto and Bernardo, trying to determine the birthday of Carla based on the month and day of her birthday, which are revealed separately to each of them.

What information does Carla give to Alberto and Bernardo?

Carla gives Alberto the month of her birthday and Bernardo the day of her birthday. Alberto knows the month, and Bernardo knows the day.

Why does Alberto initially say he doesn't know when Carla's birthday is?

Alberto says he doesn't know when Carla's birthday is because there are multiple possible dates within the month he received, and no single date can be determined immediately.

Why is Alberto confident that Bernardo doesn't know the birthday either?

Alberto is confident that Bernardo doesn't know the birthday because the months of May and June contain dates (18 and 19) that would allow Bernardo to know the birthday, but since Alberto is sure that Bernardo doesn’t know, those months must be ruled out.

What can we conclude from Alberto's statement about Bernardo not knowing?

From Alberto's statement, we can conclude that Carla's birthday is not in May or June because if it were, Bernardo could have deduced the birthday from the unique days (18 and 19).

What does Bernardo realize after hearing Alberto’s statement?

After hearing Alberto's statement, Bernardo deduces Carla's birthday because the days he has (14, 15, 16, 17) have been narrowed down to a smaller set of possible dates.

Why does Alberto become confident that he knows the birthday after hearing Bernardo's realization?

Alberto becomes confident because if the month he received had been August, there would still be two possible dates (15 and 17), so he could not have been sure. The fact that he is now certain means the month must be July, where only one date (16) remains.

What are the possible dates that were initially presented to Alberto and Bernardo?

The possible dates are: May 15, May 16, May 19, June 17, June 18, June 19, July 14, July 16, July 19, and August 14.

Why does Bernardo eliminate the 14th from his list of possible dates?

Bernardo eliminates the 14th because, after hearing that he now knows the birthday, he realizes that if the day had been the 14th, he would still be uncertain about the month (it could have been either July or August). Thus, the 14th day cannot be the correct day.

What is the final conclusion about Carla's birthday?

The final conclusion is that Carla's birthday is on July 16. This is deduced after all the logical steps and interactions between Alberto and Bernardo.