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Puzzle about birthday. Mathematical tasks - logic and reasoning

An extraordinary popularity has acquired a mathematical task on the network, which the Singapore TV presenter Kenneth Kong has published on its page on Facebook. The new Internet virus drew attention to the Mashable edition.

For four days record Kong shared more than five thousand Facebook users. Internet users took up the complexity of the task, as well as the remark of the TV preset as to what it is designed for fifth-graders.

The task condition is as follows.

"Albert and Bernard just met Cheryl and wanted to find out when she had a birthday. Cheryl gave them a list of ten possible dates:

Then Cheryl informed Albert, in which month she was born, and Bernardo - what date. After that, the next conversation occurred between men.

"I don't know when Sheril's birthday, but I know that Bernard doesn't know this either," Albert said.

"At first I didn't know when Sheril's birthday, but now I know," answered Bernard.

"And now I know when Sheril was born," Albert said.

So when did Cheryl have a birthday? "

The record on the Kenneta Kong page collected more than one and a half thousand comments and gained widespread in other blogs, as well as in the media. Many discussion participants recognized that they feel too stupid due to the fact that they cannot solve the task intended for the pupils of the fifth grade.

However, as it turned out two days later, the task was not an ordinary school, but an olympics. In addition, it was designed for 14-year-old students. This Cong reported representatives of the SASMO organization (Singapore and Asean Schools Math Olympiads). The TV host himself admitted that he even quarreled with his wife on the basis of discussing this task.

Later in the community of the organization Study Room appeared Solution of the task.

"To begin with, we need to find out if Albert knows a month or day. If he is famous for him, then there is no chance that Bernard knows the date of birth Cheryl. Thus, Albert knows the month.

From the first replica we know that Albert is confident that Bernard does not know the date of birth. Therefore, May and June can be excluded, since 19 number is only present in May (among the dates specified in the list), and the 18th number is only in June.

Thus, Bernard knows that May and June can be excluded.

After that, Bernard can find out the month when Sheryl was born. Dates remain on July 16, as well as on August 15 and August 17. At the same time, July 14 and August 14, it is possible to exclude, because if Sheril said Bernard, that her birthday is the 14th day, Albert could not give an accurate answer about the full date.

Subsequently, Albert stated that he, like Bernard, knows the date of birth Cheryl, then he knows that she was born in July. If this was August (we recall that Albert had data about the month), he could not say for sure, a birthday occurs on 15 or 17 August.

On Facebook a logical task for schoolchildren. For two days, the social network users shared her more than 4400 times and arranged a serious debate in the comments. Mashable drew attention to the story.

In the first record of Kennet, it was reported that the problem was assigned the level P5 - suitable for 10-year schoolchildren, but it turned out to be so difficult that he even quarreled with his wife about finding a solution. At the time of publication, he did not know the answer he himself, since the task was shown by his friend's niece.

Albert and Bernard just met Cheryl. They want to know when she has a birthday. Cheryl offered them ten possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15 and August 17. Then Cheryl said Albert month of his birth, and Bernardu is a day. After that, the dialogue took place.

Albert: I do not know when Cheryl's birthday, but I know that Bernard also does not know.
Bernard: At first I did not know when Sheril's birthday, but I know now.
Albert: Now I also know when Cheryl has a birthday.

When did Cheryl's birthday?

task text

Two days later, when the task has gained viral popularity in the network, representatives of the SASMO organization (Singapore and Asean Schools Math Olympiads - Mathematical Olympiads for Singapore and ASEAN countries have contacted and sent him a response to clarify that it is actually intended for children from 14 years (SEC 3 level).

According to SASMO representatives, for their ten-year practices, the Olympiad tasks never got into the network, because children are forbidden to use cell phones During their execution. Nevertheless, they decided to clarify the situation that the parents of the children of the P5 levels did not beat the alarm due to the fact that their child is not able to solve the problem spread over the network.

Dates are only 10, and the days are in the interval from 14 to 19. At the same time, only 18 and 19 numbers are found one time. If the birthday of Seryl on the 18th or 19th, then Bernard could immediately say a month.

But from where Albert knows that Bernard does not know the answer? If Cheryl said Albert, that was born in May or June, then her birthday can be May 19 or June 18. With this situation, Bernard can know when Cheryl has a birthday. The fact that Albert knows exactly what Bernard does not know the answer, says that May and June can be excluded, and Cheryl was born either in July or in August.

Initially, Bernard did not know when Sheril's birthday. How did he find out the answer after the Albert's replica? Of the remaining five days in July and August, varying from 15 to 17, only 14 meets twice. If Cheryl would say Bernard, that her day of birth of the 14th, then Bernard after Albert's assumption still could not give an accurate answer. The fact that he immediately understood everything, says that Cheryl was born not on the 14th. Three possible dates remain: July 16, August 15 and August 17.

After Bernard spoke, Albert found out when Cheryl had a birthday. If she told him that he was born in August, Albert could not know an accurate answer, because of the three remaining dates two comes in August. So, Cheryl was born on July 16.

the solution of the problem

Task text:

Holmes and Watson have a 10 supposed dates of attempted queen: January 2, January 5, February 3, February 4, February 6, March 1, March 2, March 1, April 1, April 3.
After finding an important witness, he gave them information in parts, Holmes he informed the month of attempt, and Watson day.

The following dialogue took place between Holmes and Watson:
1. Holmes: I am unknowing the date of the attempt, but I know what you do not know.
2. Watson: Now I know the date.
3. Holmes: Now I also know.

Question: When will an attempted attempt?

The solution of the problem:

For convenience, we have a duty of the attempts as follows:

January 2, January 5;
February 3, February 4, February 6;
March 1, March 2, March 4;
April 1, April 3.

The dialogue between Holmes and Watson is divided into three strictly followed by a replica, and it is necessary to solve the task that seems consistently analyzing each phrase from the dialogue. So, Holmes is known month attempts and watson day:

  1. Holmes: I am unknown the date of the attempt, but I know what you do not know. I would like to add that before that Holmes and Watson did not communicate in any way. At the same time, Holmes definite I am sure that Watson unknown accurate date Attempt. In which Watson would know the exact date of the attempt, knowing only the day? Of all dates, only two numbers are repeated: 5 January and February 6. So, Holmes knows the month of the attempt, and the fact that Watson does not know accurate date. The first replica gives us to understand that the month is definitely not January and not February.
  2. Watson: Now I know the date.The following dates remained:
    March 1, March 2, March 4;
    April 1, April 3.
    Having dropped January and February, Watson understood an unequivocal answer - it means the number he knew was in January and February and was repeated in the other months (2nd, 3, 4). The second replica gave to understand that the number is definitely not 1.
    The mistake of many readers is that they discard the third phrase and begin to analyze only the first two, because Watson understood the answer, it means that, in their opinion, they will be able to solve a riddle. But without the third phrase, the task cannot have deciable solution!
  3. Holmes: Now I know too. Replica Watson gave Holmes to understand that this is not a 1 number. In which case, knowing the month, Holmes can give a definite answer? Only in the event that this is April! After all, in April, there was only one date - April 3. If the date of the attempted was in March, after the replica of Watson, Holmes would not be able to know the answer, because in March, in addition to the first two more numbers remained - 2 and 4, and at the same time it doesn't matter that Watson already knows the date.

When did Cheryl's birthday?

Analogue of this task is its more famous option, which Singapore TV presenter Kenneth Kong once blew up the Internet. Here is its contents:

Albert and Bernard just met Cheryl. They want to know when she has a birthday. Cheryl offered them ten possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15 and August 17. Then Cheryl said Albert month of his birth, and Bernardu is a day. After that, the dialogue took place.

Albert: I do not know when Cheryl's birthday, but I know that Bernard also does not know.
Bernard: At first I did not know when Sheril's birthday, but I know now.
Albert: Now I also know when Cheryl has a birthday.

When did Cheryl's birthday?

You have already understood how to solve the task about Holmes and Watson, now try to determine when Cheryl's birthday 🙂

  1. 1 Associate Professor:

    Sorry, but perhaps it is appropriate here a little humor in connection with the challenge about a birthday. Namely, the famous task of the Gashek's Gashek, who is taught by the mouth of his character Svweyk Consilium doctors:
    …
    The case was completely clear. Thanks to the Schweki made, on its own aspiration, a statement whole line The questions disappeared and left only a few most important. The answers to them were to confirm the initial opinion about Sewing, compiled on the basis of the doctor of the doctor of Psychiatry Cadlerson, Dr. Geveroha and Englishman Vaiking.
    - Radium is heavier tin?
    "I apologize to him, I did not hang out," Schweik answered with his cute smile.
    - Do you believe in the end of the world?
    - Before, I have to see this end. But, in any case, tomorrow he will not be, - Carelessly threw Sew.
    - And you could calculate the diameter globe?
    "I apologize, I could not," Schweik said. "However, I also want, gentlemen, ask you one riddle," he continued. "It costs a four-storey house, in every floor in eight windows, on the roof - two hearing windows and two pipes, and two hearing windows. In each floor there are two apartments. And now tell me, gentlemen, in what year did a grandmother died at the Swiss?

  2. 2 Arman:

    Everything is very simple here.
    It is clear that since Bernard is silent, it means that 18 and 19 are not dates of DR (they are found only one time), otherwise he would immediately told the date.
    Now after Albert declares that there is no idea when Dr., then Bernard thinks:
    DR is not exactly 19 May and not in June (if it were June, then Albert would immediately say that he knows after the silence of Bernard) - Thus, June 17 is also excluded

    Now if the date was 14, 15 or 16, they would be in two months and Bernard could not say what he knows now. He would have to choose from two months.
    Only one option remains - it is August 17th. After he said, he knows exactly the date, then Albert spent the same reasoning and said that now also knows the date.

  3. 3 bio:

    The solution of the task is not built on the "calculation" of the date. And on the discard of the dates, which could not cause the dialogue specified in the condition.

    For example, DR 17yunya would cause the following dialogue:
    Bernard: "I don't know when Sheril's DR (chooses between 17.06 and 17.08)
    Albert: "Then I know - 17.06" (choosing between 17.06 and 18.06 remember that 18.06 Bernard would immediately calculate DR)

  4. 4 Guest063:

    Here is the answer: August 17.
    By condition 18 and 19 we remove. Two pairs remain - 14,15,16,17. Albert thinks and says that he does not know, and does not know Bernard. Begins to think Bernard gives an answer. What he had reasoning: 14, 15, 16 numbers - pair, on them guess the date relying on the terms of the task is impossible, the number 17 remains : Albert says that he does not know because in August three numbers, so you can't call it exactly and says that Bernard does not know too, because the number 17 is available both in June and in August, so it's not possible to call a date. So far, the task condition is observed. Bernard begins to think further. Number 17. Maybe in June? But then Albert would immediately give an answer (then the condition of the task would be disturbed), so it is not June. So this is August. The number 17 remained only in August. Answer: August 17. Verification Conditions: 1. At first, Albert does not know the dates and does not know Bernard. 2. Learn Bernard. 3. Finds Albert (delivering himself to the place of Bernard). Answer: August 17.
    Why we remove May 19 and June 18 I will try to explain to you. If Seryl had a birthday on May 19, then she would have to Albert to say the month of May, and Bernardu number 19. Then the word takes Albert and says that he does not know the date of birth Cheryl and also says that Bernard does not know her either. Here, just the condition of the task is disturbed. I explain why: Albert says that he doesn't know the date of birth, since in the month of May three numbers, but about the fact that Bernard does not know the dates he would have been able to say, but I would have violated the condition of the task, since Bernard knows exactly the date of birth and It is 19 May (since under the condition of the task number 19 one). The same with the date is June 18.

  5. 5 Artem:

    A somewhat different option is possible. The problem of the problem is limited by the Albert monologue and does not change it. After Cheryl whispered on Albert's ear, and Bernardum is the number of his birthday, Albert said: "Bernard does not know, and I know the date of birth." Singapore schoolboy argues so. Alberta was named July or August, otherwise he would have doubts, since Cheryl could call Bernard number 19 or 18, which in the list correspond to May or June. Bernard would definitely define the date of birth, if he was named the number 14, for it repeats in July and August. So albert thinks and thinks a schoolboy, otherwise why was it whisper on the ear. Dates remain: July 16, or 15 and 17 August. For a student, history is repeated, Augustus, he excludes from the list, because Albert could not determine the date. The only option remains - Cheryl's birthday on July 16.

    Guest063 reply:
    April 26th, 2015 at 0:57

    And where under the condition Albert stated: "Bernard does not know, and I know the date of birth"? By condition, Albert says: "I don't know when Sheril's birthday, but I know that the Bernard does not know this" and one more time: "Then I also know when Sheril's birthday," but after the words of Bernard: "At first I did not know when Sheril's birthday, but now I know it." THIS CONDITION. The point is not that Cheryl could call Bernard number 19 or 18, which correspond to May or June, and that if Sheril called the number 19 or number 18, then Bernard would immediately call the date of her birth, but by the terms of the task Albert He says that he himself does not know and knows Bernard, because Albert is confident that if Seryl would call Bernard number 19 or 18, then Bernard would first have started a conversation. And in the end we would not have seen the condition of the task that we see. Albert could not say on the condition of the task: "I don't know when Sheril's birthday, but I know that the Bernard does not know that."
    Please explain to me where you are when solving the task of the date - May 15, May 16 and June 17? What's this? Based on the fact that the number 19 is present in May, and in June number 18? Please explain your logic why they removed, and not that ("unique numbers"), which is present on the "Internet" and which no one can explain to explain. This is the task. It needs to be solved. And it turns out that on June 16, somehow (with the help of "unique numbers"), it was adjusted under the answer of the problem.

  6. 6 Artem:

    Publication of the task of the TV host Kennet Kong caused an increased interest and a large flow of discussions. The reason is clear: the solution does not require special knowledge in mathematics, but at the same time it is necessary to use non-standard logical thinking, the option of which is not specified in condition. In addition to the above, my personal opinion: the dialogue of the tasks of the task is incorrectly formulated. First, Albert may, without waiting for the replica of Bernard, to determine the date of birth of Cheryl. Therefore, his initial statement that he does not know the date is incorrect. Here the author of the task is clearly wrong. Secondly, the phrase of Bernard: "At first I did not know when I cheryl's birthday, but now I know it," does not carry it for more information Nor Alberta nor a schoolboy decisive task. They can determine the date of birth without his participation in the conversation. How to do this is described by me in the fifth comment.
    I answer your question Guest063. Albert knows only a month of birth. Therefore, his statement that Bernard does not know the date of birth, removes the months of May and June from the list, in which there are "exceptional" dates. Then you need to drop out of the remaining months of dates with a repeated number (July 14 and 14 for Bernard) and a month (August 15, August 17 for Alberta). Then the only date remains on July 16, otherwise the task has no solution.

  7. 7 Vasil Stryzhak:

    Obviously, many remember the Russian folk finching game "Soroka-Raven Kashov", which allows you to train small motor hands kids. In my opinion, it is not only funny fun for small, but also logical task For more adults.
    The forty-crow porch was cooked, on the threshold of the jump, guests convened. The guests were not, the porridge was not meant. All his porridge forty-crow kids gave. This gave that this was given, this was given, this was given, and this did not give it: he was small, the croup was not dragged, he did not drink firewood, did not wear the water.
    How many porridge porrows a crow?

  8. 8 Vasil Stryzhak:

    There are several options for text. finger Games "Forty-crow Kasha cooked." Came to the conclusion: the next version is somewhat better suited to the logical task.
    Soroka-Rust Kashka cooked, kids fed. This gave that this was given, this was given, this was given, and this did not give it: you were small, the croup did not dravly, the firewood did not drink, did not wear the water.
    How many porridge porrows a crow?

  9. 9 Vasil Stryzhak:

    Due to the fact that in the formulation of a logical problem, the text from the Finger Game "Forty-Raven Kashov" was used, the solutions methods may be different depending on the argument approaches. As the author of the question, I propose my version related to the capacity of cutlery, which does not exclude possible other options for determining an acceptable result.
    Forty crow like thoughtful mother, Cook porridge for all his children, taking into account to divide it on equal portions to each child. Since kids small can be assumed: the portion corresponded to the volume of one chuminous - a wooden cook spoon with a long handle used in ancient in Russia. The capacity of this kitchen utensils is difficult because in those times it was done manually. Modern midnisters (cooks) for distribution of food have a volume of 100 ml and more.
    If you follow the text, she did not give porridge to the small slackere. Then, it was obvious that his portion was divided between the remaining four brothers. This action She could do a tablespoon, each at least one spoon of porridge. According to the table provided by Wikipedia, the standard volume of Art. spoons 18 ml. Of the more dense products, such as milk or sugar (you can learn porridge) Art. A spoon holds 20 grams without a slide, and with a slide - 25. Consequently, one portion of porridge 25 x 4 \u003d 100 grams (options in 200, 300, etc. are suitable for large children or adults). This conclusion seems to be consistent with the capacity of the cheware. As a result, five servings are 500 grams of porridge welded with a raven.

  10. 10 Valeriystepmn:

    1. It is clear that Cheryl did not tell Bernard's number 18 and 19, otherwise Bernard immediately called the birthday of June 18 or 19, respectively (because numbers 18 and 19 are not repeated in other months). But Bernard is silent. So, on June 18 and 19, we exclude.

    2. It is clear that Cheryl did not tell Albert month June, otherwise Albert would immediately call birthday on June 17 (since another possible date of June 18 is excluded, see paragraph 1). But Albert is silent. So month we exclude a month.

    3. Bernard argues that it knows exactly a birthday. It can only be in one case, if Cheryl told him the number 17. The number 17 is present in June and August, but June is excluded (see paragraph 2). So birthday is August 17.
    If you suggest that Cheryl said Bernard's other possible numbers 14, 15, 16, then Bernard could not argue that she knew for a birthday, because these numbers are repeated twice in different months.

    4. It is clear that Cheryl could say Albert one of three possible months - May, July or August (June is excluded, see paragraph 2). But in each of these months a few dates, so Albert says that he does not know the birthday.
    Albert does not know what number Cheryl said Bernarda. Albert only knows that it can be numbers 14, 15, 16, 17.
    Albert talks like this: numbers 14, 15, 16 are present in two different months and therefore Bernard (if he hears them from Cheryl) will not be able to determine the birthday. But Bernard argues that she knows exactly a birthday. Albert guess that Bernard was able to accurately determine the birthday only if Sheril called him the number 17. Because On June 17, we are excluded (see paragraph 2), then the birthday of August 17. Now Albert knows the birthday of Cheryl.

    Valery Ivanovich

  11. 11 Valeriystepmn:

    "Cheerful" solution:

    Indeed, if Cheryl tells Bernard's number 18 or 19, since these numbers are not repeated in other months, then it actually calls Bernard his D.R. June 18 and May 19, respectively. Bernard remains only to voice her answer. But Bernard is silent, and therefore Albert concludes that Cheryl did not speak Bernard's number 18, 19.

    2. Month June is excluded.

    Indeed, if Sheril called Albert month June, then Albert would immediately define her D.P. - June 17 (because the date on June 18 is excluded, see paragraph 1). Since Albert did not name D.R., then Bernard concludes that Cheryl did not tell Albert month June.

    Bernard could hear from Cheryl one of the numbers: 14, 15, 16, 17 (numbers 18, 19 are excluded, see paragraph 1). Only number 17 allows Bernard to determine D.R. - August 17 (since June June is excluded, see paragraph 2). Numbers 14, 15, 16 do not allow Bernard to determine D.R., because Twice repeated in different months.
    Since Bernard said that he knows D.R., then this means that Cheryl told him the number 17, and according to D.R. - August 17.

    4. Albert knows only a month. Therefore, it cannot determine D.R., because In each month several dates. Albert believes that Bernard will not be able to determine D.R., because Each number 14, 15, 16, 17 is repeated twice in different months. But Bernard says that he knows D.R. Albert guess that Bernard was able to determine D.R. Only in one case, if Sheril was told by the number 17. Since June is excluded, then D.R. - August 17. Now Albert knows D.R. Sheril.

  12. 12 Mike:

    You have a mistake at the very beginning - not only June, but also May. Therefore, on last stage Albert chooses between three options: July 16, 15 and 17 August. Augustus disappears and the correct answer: July 16. This task has already been a million times already in the Internet.

  13. 13 Valeriystepmn:

    No error.
    If you are talking about SASMO Solution (Singapore and Asean Schools Math Olympiads) with their answer on July 16, then it is not true, since from the very beginning it is built on a false send.

  14. 14 Valeriystepmn:

    Final solution:

    1. Event: "Cheryl says Bernard number 19 or 18" is excluded because it contradicts common sense. Accordingly, the date May 19 and June 18 are excluded from the list possible days birth.

    Indeed, if Cheryl says Bernard's number 19 or 18, then actually she calls Bernard his D.R. (Since these numbers are not repeated in other months), and Bernard remains only to voice her answer - May 19 or June 18, respectively. Then the task loses any meaning, because Cheryl itself sets the question and herself answers it.
    Therefore, the event: "Cheryl says Bernardum Number 19 or 18" is excluded and, accordingly, the date on May 19 and June 18 are excluded from the list of possible D.R.

    2. Month June is excluded. Possible numbers 14, 15, 16, 17 (numbers 18, 19 are excluded, see paragraph 1).

    When Albert says: "I don't know when you have a birthday," then it means that Cheryl did not call him a month June.
    Indeed, if Cheryl calls Albert month June, then Albert immediately defines D.R. June 17 (since the date of June 18 is excluded, see paragraph 1), and he does not know. This means that Cheryl did not say Albert month June. Albert's statement allows Bernarda to also conclude that the priest did not call Albert month June (according to the same logical grounds).

    4. Bernard declares that D.R knows This is possible only in one case, if Cheryl called him a number 17. Accordingly, D.R on August 17 (the date is excluded on June 17, since June is excluded, see paragraph 2). Numbers 14, 15, 16 twice repeated in different months, so Identify D.R. It is impossible for these numbers.

    5. Albert, having heard that Bernard knows D.R., guesses what it is possible only if Sheril said Bernardum number 17 and respectively D.R. August 17. (Date on June 17 is excluded, because June is excluded, see paragraph 2). Numbers 14, 15, 16 twice repeated in different months, so Identify D.R. It is impossible for these numbers.
    So he says: "Great, now I know!"

  15. 15 Valeriystepmn:

    1. SASMO solution (Singapore and Asean Schools Math Olympiads) (reply - July 16) is built on the assumption that Cheryl can call Bernard's number 18 or 19 (i.e., on the assumption that Cheryl immediately after his tip can actually call Bernard My birthday. In other words, Cheryl asks the question and herself does not answer him. Bernard remains only to voice her answer). If it does not bother you, then feel free to write the answer - July 16.

    2. I consider such an assumption deprived of every common sense. Therefore, in my decision (answer - August 17) this possibility is excluded immediately.

  16. 16 Mike:

    You have absolutely not mathematical argument when you exclude the possibility that Cheryl could not call the numbers 18 and 19 Bernard. Mathematics is interesting exactly what allows you to work with the concepts. Without "common sense" from everyday point of view!

  17. 17 Valeriystepmn:

    You say: "Mathematics is interesting exactly what allows you to work with the concepts. not having "common sense" ... "
    You did not confuse anything? This is the task of logic! At the same time, no one forbids you to use one or another mathematical apparatus.

    Now about the absence of mathematical argument. It is about the method of solving problems. Even schoolchildren know that the solutions of the equations determine OD. (region permissible values). So in logical tasks, you must first exclude events in which the task loses any meaning. And only then you can build your logic chains. Moreover, when solving the task, these excluded events cannot be used as possible.

    In our logical task there is such an event that should immediately exclude - this "Cheryl says Bernard number 19 or 18". After all, Cheryl is not just a tsiferki calls, but actually gives the answer to his own rebus. The task is to lose all meaning. So think logically! Is such an event or not? Should we exclude this situation from consideration or not?

    As I understood, you consider it possible to build conclusions on the basis of events in which the task loses any meaning. Then your answer, indeed, July 16th. I immediately exclude such events from the list of possible events and I get the answer - August 17.

    P.S. It is unacceptable to build conclusions on Rotina Foundation. What is the foundation - this is the result.

  18. 18 Mike:

    To your information, mathematical (abstract) logic takes place with all possible events, including those that, from the point of view of "common sense, could be excluded. Therefore, your solution based on "common sense" may be interesting for psychologists, future investigators, but completely unacceptably just from the point of view of mathematical logic.

  19. 19 Valeriystepmn:

    You say: "... Mathematical (abstract) logic takes place with all possible events, including those that, from the point of view of" common sense, could be excluded. Therefore, your solution based on a "common sense" may be interesting for psychologists, future investigators, but completely unacceptably just from the point of view of mathematical logic. "

    So we have quite well here. life situation: Boys, Girl, Question Guessing. We are just offered to work as an investigator, and not an arithmometer, as you suggest everyone here, which is stupid! Rides all options.

    P.S. You say that the decision proposed by me is "completely unacceptable ... from the point of view of mathematical logic." I want to notice you that any mathematical tool must be applied with the mind.

  20. 20 Valeriystepmn:

    Looks like you have your own (human) logic have long been replaced with mathematical (abstract). And the arguments now give you mathematical. Otherwise, this is, of course, not an argument, by definition.

    In essence, you are talking like this: I will not exclude an event "Cheryl says Bernard's number 19 or 18", because your argument ("task loses any meaning") - a non -monatic. I still will take this event in the process of my decision. Okay. But what actually do you want to solve? The answer was already Cheryl actually gave.

    It seems I understood why you do not want to exclude this event - because the mathematical logic whispered to you that Cheryl is a complete fool and you can expect anything, for example, it can give a response to Bernard before the task is sounded.

    Again does not pass! Mathematical logic was to formulate it mathematically. Just some kind of ambush!

    P.S. Do not forget that this is just a logical task, compiled for schoolchildren. To solve this problem, there is no need to attract additional mathematical instruments - ordinary logic is quite enough. By the way, in a Singapore solution also uses ordinary logic (although they are slightly talked).

    And leave alone mathematical logic! She is not guilty of anything! - People who are inappropriately use it are to blame (it is not afraid of it without parsing). As the Ostap Bender spoke in the "Golden Calf": "And do not eat raw tomatoes for the night, so as not to cause harm ... reason"

  21. 21 ValeryStepmn:


    Indeed, if Cheryl tells Bernard's number 18 or 19, then in fact it gives an answer to the question of the task. This contradicts common logic.
    Therefore, June 18 and May 19 are excluded from the list of dates at the very beginning of the decision.



    Therefore, the month of June is excluded and, accordingly, on June 17, it is excluded from the date of the birth.



    Therefore, the month of August is excluded and, accordingly, on August 14, August 15, August 17, are excluded from the date of the birth.



    But after the statement of Albert, it became clear that only two months of May and July were possible, and there are two non-repeated numbers 14 and 15 (August 14 and August 15, see clause 3).
    Since Bernard says that D.R knows now, it means that Cheryl called him 14 or 15. If Cheryl said 14, then Bernard determines D.R. the 14 th of July. If Cheryl said 15, then Bernard determines D.R. May 15.
    In any case, the date of birth is unknown to us, because It is not known which of the numbers 14 or 15 Cheryl called Bernard.


    This is an incorrect statement, because Albert does not know what number Cheryl called Bernard 14 or 15. And if so, Albert cannot determine D.R.

    Valery Ivanovich

  22. 22 Victor:

    In this wonderful task there is uncertainty consisting in the following. Albert's first statement that Bertrand does not know the correct answer is based on observation (posteriorio) or is it a priori (we know this without observation of bertrans)? The subsequent logic and the solution of the problem depends on this question. If we proceed from the fact that Albert's knowledge is a priori, then it is possible only if the month of birth or July either August (since in May and June there are dates 18 and 19 that definitely determine the answer). Well, then the entire logic of solving the problem is built. And what if the knowledge of Albert is a posteriorio, that is, he does a judgment based on the reaction of Berran. Then it is quite possible that Alberta called May and he, seeing that Bertran did not know the answer, admits that he also did not know the answer. Then Bertrand concludes that the month of birth is not June, so we come to August 17th.

  23. 23 ValeryStepmn:

    I saw my mistake, but you, Victor, seem to do not even understand that this task has no solution.

    By the way, Cheryl could well name Albert month May - read carefully my post â„–21 - everything is quite clearly clarified.

    Valery Ivanovich.

    P.S. If you are questions, contact.

  24. 24 ValeryStepmn:

    Victor, warning in advance that my decision set out in post â„–21 was designed for people with obstection logic - everyone else, please do not worry and pass by (first of all it concerns lovers of stupid parties of all possible and impossible (from the point of view of common logic) options).

    My conclusion: the task is made incorrect and therefore does not have a solution.

  25. 25 ValeryStepmn:

    Final solution.

    This Singapore logical task "Sheril's birthday" is incorrect and therefore has no solution.

    1. Immediately exclude events: "Cheryl says Bernard number 18 or 19" and these events cannot be considered in the decision-making process as possible.
    Indeed, if Cheryl tells Bernard's number 18 or 19, then in fact it gives an answer to the question of the task. This contradicts common sense (sevene logic).

    2. Albert says: "I do not know ..."
    This means that Cheryl did not call him a month June, otherwise Albert immediately called D.R. June 17 (t.k. June 18 is excluded, see paragraph 1).

    3. Albert says: "... But I know that Bernard does not know."
    This means that Cheryl did not name Albert in August, because in August there is a non-repeating number 17 (June 17, see paragraph 2) and then was the likelihood that Bernard could know - if Sheril called Bernard number 17, then Bernard Immediately called D.R. August 17.

    Therefore, the month of August is excluded and, accordingly, on August 14, August 15, August 17, are excluded from the date of the birth.

    4. Thus, months June and August are excluded (see paragraphs 2 and 3). Accordingly, Cheryl could say Albert May or July.

    5. Bernard says: "At first I did not know, and now I know."
    After tip, Cheryl, Bernard really did not know D.R., because Each number has its own "twin" in another month.

    But after the statement of Albert, it became clear that only two months of May and July were possible, and there are two non-repeated numbers 14 and 15 (August 14 and August 15, see clause 3).

    Since Bernard says that D.R knows now, it means that Cheryl called him 14 or 15. If Cheryl said 14, then Bernard determines D.R. the 14 th of July. If Cheryl said 15, then Bernard determines D.R. May 15.

    In any case, the date of birth is unknown to us, because It is not known which of the numbers 14 or 15 Cheryl called Bernard.

    6. Albert says: "Excellent, now I know!"
    Albert does not know what number Cheryl called Bernard 14 or 15, but he knows the month. Therefore, now Albert knows D.R.

    And in this case, the date of birth is unknown to us.

    Answer: no solution, because The task is incorrect.

    Valery Ivanovich