Logical task. Math problems - logic and reasoning

24.06.2019

On April 11, Singaporean TV presenter Kenneth Kong posted a logic puzzle for schoolchildren on his Facebook. In two days, social network users shared it more than 4400 times and staged a serious debate in the comments.

Kenneth's first post reported that the problem was rated P5 - suitable for 10-year-olds, but it turned out to be so difficult that he even quarreled with his wife about finding a solution. At the time of the publication of the picture, he himself did not know the answer, since the problem was shown to him by his friend's niece.

Task text:

Albert and Bernard just met Cheryl. They want to know when her birthday is. 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. Sherrill then told Albert the month of her birth and Bernard the day. After that, a dialogue took place.

Albert: I don't know when Cheryl's birthday, but I know that Bernard doesn't know either.
Bernard: At first I didn't know when Cheryl's birthday was, but now I know.
Albert: Now I also know when Cheryl's birthday.

When is Cheryl's birthday?

Two days later, when the task became viral on the network, representatives of the SASMO organization (Singapore and Asean Schools Math Olympiads) contacted Kenneth and sent him an answer, clarifying that it was actually intended for children from 14 years (level Sec 3).

According to SASMO representatives, during their ten-year practice, the Olympiad tasks have never made it onto the network, because children are not allowed to use mobile phones while they are doing them. Nevertheless, they decided to clarify the situation so that parents of P5 children would not sound the alarm that their child was unable to solve a problem that had spread across the network.

The solution of the problem:

There are only 10 dates, and the days are in the range from 14 to 19. At the same time, only the 18th and 19th numbers occur once. If Cheryl's birthday is on the 18th or 19th, then Bernard could tell the month right away.

But how does Albert know that Bernard doesn't know the answer? If Cheryl told Albert that she was born in May or June, then her birthday could be May 19 or June 18. In this case, Bernard can know when Cheryl's birthday. The fact that Albert knows for sure that Bernard does not know the answer suggests that May and June can be excluded, and Cheryl was born either in July or August.

Initially, Bernard did not know when Cheryl's birthday was. How did he know the answer after Albert's remark? Of the remaining five dates in July and August, ranging from 15 to 17, only 14 occurs twice. If Cheryl told Bernard that her birthday was on the 14th, then Bernard, after Albert's assumption, still could not give an exact answer. The fact that he immediately understood everything suggests that Cheryl was not born on the 14th. There are three possible dates left: July 16, August 15 and August 17.

After Bernard spoke up, Albert found out when Cheryl's birthday was. If she had told him that she was born in August, Albert would not have known the exact answer, because of the three remaining dates, two are in August. So Cheryl was born on July 16th.

Following the dress incident in late February, which split netizens into two warring camps, controversial content has become increasingly popular on the Internet. Many commentators on Kong's page published voluminous calculations and calculations, but managed to arrive at the wrong answer. About half of them claimed that Cheryl was born on August 17, but there were other options.

Posted by Artem of 93 Mon, 05/04/2015 - 08:29

In response to your cry (judging by the punctuation marks and "caps"), I would like to quote the comment below from "Foxi":

If Cheryl had named the number "19" or "18", Bernard would have immediately recognized the month, because the numbers "18" and "19" are used only once in the table. Therefore, from the words spoken by Albert, we can conclude that Cheryl told him not "May" and not "June", otherwise there would be a chance that Bernard would immediately guess when her birthday is. And since Albert is sure that Bernard is not aware of Cheryl's date of birth, it means that this is not "May" and not "June".

And I will also quote myself from the comment below:

The fact is that the 18th and 19th numbers occur only once among the set of all possible dates. And if, for example, Cheryl's birthday falls on May, then Albert can no longer guarantee that Bernard does not know the desired date. After all, if Bernard was informed that his birthday falls on the 19th, then it becomes obvious that it is May 19th. But Albert knows for sure that Bernard cannot exactly name this date. And if this day fell on another date in May, then Albert would argue that Bernard probably knows when Cheryl's birthday. But that's not what he said. So Cheryl's birthday is definitely not in May.

to answer

Posted by Guest063 Mon, 05/04/2015 - 15:46

Dear Artem of 93, please make a full explanation of the texts you wrote, namely: №1. "Therefore, from the words spoken by Albert, we can conclude that Cheryl did not tell him" May "and not" June ", otherwise there would be a chance that Bernard would immediately guess when her birthday is." And number 2. : "And if this day fell on another date in May, then Albert would have argued that Bernard might know when Cheryl's birthday is."
I wonder how you in text # 1 (one) conclude "that Cheryl told him not" May "and not" June ", otherwise there would have been a chance"? You do not unreasonably exclude whole dates (or do you rely on how they write in most Internet resources? Like "Unique numbers", with the help of which whole MONTHS are removed!). This is a Math problem for schoolchildren (the "Olympiad" problem)! And even more interesting is your text # 2 (two). Let me propose to you, for example, that Cheryl told Albert the month of MAY, and Bernard the number 15. And how do you do it: "then Albert would claim that Bernard might know when Cheryl's birthday is." Is that how Bernard "might have known"? And now Bernard knows the number 15. So what? BY THE CONDITION OF THE PROBLEM, numbers 15 - two (2) are MONTH MAY and MONTH AUGUST. How did Bernard "possibly know ..."? Is he reading Cheryl's mind? And ALBERT, in the first place, would not be able to assert that Bernard, perhaps, knows ... "And all because, BY THE CONDITION OF THE PROBLEM, the numbers 15 are paired, like all the remaining numbers. And how the PROBLEM is solved, I wrote above. explanations of why this or that number does not fit, and which one fits. The whole solution is based on the CONDITION OF THE PROBLEM. And if you noticed, then I did not rely on the INITIATED "UNIQUE NUMBERS" by which you can remove WHOLE MONTHS. adheres to the answer on JULY 16, cannot explain why they remove the WHOLE MAY and the remaining JUNE 17! unnatural, with "Unique numbers", according to which the answer is "adjusted" to 16 JULY.
At least before you write to me, you solved this problem by applying conditions to all numbers. And I think you would then understand that the answer is 17 AUGUST. Only for this the problem must be solved!

to answer

Posted by Artem of 93 Mon, 05/04/2015 - 17:32

Guest063, the fact is that I solved this problem. Before writing comments on it, I thoroughly delved into the condition and solution, and also built tables in Excel. After that, I was convinced of the correctness of the solution presented here.

Now about the May and June dates. Let Cheryl's birthday fall on May 19th. Albert knows that Bernard has been given a number, but does not know which one. At the same time, Albert was told that the desired date was in May. Albert realizes that Cheryl's birthday may fall on May 15, 16 or 19. The exact date is unknown to him. But Albert can tell if there is a chance that Bernard can give an exact date. And there is such a chance, since Albert understands that if Bernard was informed that his birthday falls on the 19th, then Bernard already knows the month. Hence, Albert cannot claim that Bernard does not know this date. And in our problem, he claims that Bernard will definitely not be able to give the exact date. So the birthday is definitely not in May. The situation is similar with June dates.

to answer

Posted by Guest063 Tue, 05/05/2015 - 15:09

Artem of 93 let's talk from the very beginning. CHERYL tells ALBERT the "month" of his birthday. CHERYL tells BERNARD the "day" of his birthday. Further Silence ... Albert is silent (thinks). Bernard is silent (thinks). Albert starts a conversation. He says that he himself does not know and does not know Bernard when DR is with Cheryl. Why does Albert say so? Because if Cheryl had told Bernard the number 19 or 18, then Bernard WOULD NOT BE SILENT THEN, BUT IMMEDIATELY WOULD CALL THE DATE OF BIRTH. And we would not have the continuation of this task. AND BY THE CONDITION OF THE PROBLEM, ALBERT DOESN'T KNOW AND DOESN'T KNOW BERNARD. THIS IS THE CONDITION OF THE PROBLEM !!! And as soon as Albert said his first phrase, we can safely remove the numbers 19 and 18 (AND ONLY THESE NUMBERS), since the DR date is not exactly related to these numbers. They will no longer participate in solving the PROBLEM. These numbers, in no way contribute to the fact that someone could remove WHOLE MONTHS (MAY and JUNE). THIS IS A Math PROBLEM! It has several conditions. These conditions must first be FINDED. Then they must be clearly OBSERVED! And how to further SOLVE THE PROBLEM, I wrote above.

On April 11, Singaporean TV presenter Kenneth Kong posted a logic puzzle for schoolchildren on his Facebook. In two days, users of the social network shared it more than 4400 times and made serious d :) in the comments.

After at the end of February, which divided netizens into two warring camps, content that causes controversy between users is increasingly gaining popularity on the Internet. Many commentators on Kong's page published voluminous calculations and calculations, but managed to arrive at the wrong answer. About half of them claimed that Cheryl was born on August 17, but there were other options.

Actually, the task itself:
Albert and Bernard just met Cheryl. They want to know when her birthday is. 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. Sherrill then told Albert the month of her birth and Bernard the day. After that, a dialogue took place.

Albert: I don't know when Cheryl's birthday, but I know that Bernard doesn't know either.
Bernard: At first I didn't know when Cheryl's birthday was, but now I know.
Albert: Now I also know when Cheryl's birthday.

When is Cheryl's birthday?

Source: TJ

P.S. I will publish the answer in 15 minutes;)

Updated 14/04/15 20:27:

The solution of the problem

There are only 10 dates, and the days are in the range from 14 to 19. At the same time, only the 18th and 19th numbers occur once. If Cheryl's birthday is on the 18th or 19th, then Bernard could tell the month right away.

But how does Albert know that Bernard doesn't know the answer? If Cheryl told Albert that she was born in May or June, then her birthday could be May 19 or June 18. In this situation, Bernard might know when Cheryl's birthday is. The fact that Albert knows for sure that Bernard does not know the answer suggests that May and June can be excluded, and Cheryl was born in either July or August.

Initially, Bernard did not know when Cheryl's birthday was. How did he know the answer after Albert's remark? Of the remaining five dates in July and August, ranging from 15 to 17, only 14 occurs twice. If Cheryl told Bernard that her birthday was on the 14th, then Bernard, after Albert's assumption, still could not give an exact answer. The fact that he immediately understood everything suggests that Cheryl was not born on the 14th. There are three possible dates left: July 16, August 15 and August 17.

After Bernard spoke up, Albert found out when Cheryl's birthday was. If she had told him that she was born in August, Albert would not have known the exact answer, because of the three remaining dates, two are in August. So Cheryl was born on July 16.

The task turned out to be simple, over which I thought indecently for a long time, I hope, not the only one. :) Long life and prosperity to all!

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

A task

Albert and Bernard just met Cheryl. They want to know when her birthday is. 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. Sherrill then told Albert the month of her birth and Bernard the day. After that, a dialogue took place.

Albert: I don't know when Cheryl's birthday, but I know that Bernard doesn't know either.

Bernard: At first I didn't know when Cheryl's birthday was, but now I know.

Albert: Now I also know when Cheryl's birthday.

When is Cheryl's birthday?

Solution

There are only 10 dates, and the days are in the range from 14 to 19. At the same time, only the 18th and 19th numbers occur once. If Cheryl's birthday is on the 18th or 19th, then Bernard could tell the month right away.

But how does Albert know that Bernard doesn't know the answer? If Cheryl told Albert that she was born in May or June, then her birthday could be May 19 or June 18. In this case, Bernard can know when Cheryl's birthday. The fact that Albert knows for sure that Bernard does not know the answer suggests that May and June can be excluded, and Cheryl was born either in July or August.

Initially, Bernard did not know when Cheryl's birthday was. How did he know the answer after Albert's remark? Of the remaining five dates in July and August, ranging from 15 to 17, only 14 occurs twice. If Cheryl told Bernard that her birthday was on the 14th, then Bernard, after Albert's assumption, still could not give an exact answer. The fact that he immediately understood everything suggests that Cheryl was not born on the 14th. There are three possible dates left: July 16, August 15 and August 17.

After Bernard spoke up, Albert found out when Cheryl's birthday was. If she had told him that she was born in August, Albert would not have known the exact answer, because of the three remaining dates, two are in August. So Cheryl was born on July 16th.

Birthday is a date consisting of a day and a month. Cheryl wrote 10 dates. They are in the problem statement. Four numbers of dates are repeated - these are 14, 15, 16, 17. They are in different months. Two numbers of dates do not repeat - these are 18, 19. Sherrill gave Albert only the month of her birthday, and Bernard only gave her birthday. Albert and Bernard look at the dates in the months that Cheryl wrote to them and ponder what can be learned from this to find out when her birthday. 1) Albert thinks like this. If Cheryl told Bernard the number 18 or 19, he would immediately say that he knows when her birthday is. 18 and 19 occur once in months, these are unpaired numbers, they do not repeat in other months. These are the dates "May 19" and "June 18". But Bernard is silent. Albert concludes that Cheryl's birthday is on a different day. He crosses out the dates: "May 19" and "June 18". Albert realizes that Bernard crossed them out too. 2) Only paired numbers remain, which occur more than once in months. In June, there is only one date "June 17" after deleting "June 18". If Cheryl had named Albert the month "June", he would have said without hesitation that he knew when her birthday was, and it would have been "June 17". But he does not say this, from which we can conclude that Cheryl told him some other month, either May, or July, or August. Albert crosses out the date "June 17". Albert realizes that Bernard does not yet know the date - Cheryl's birthday, since he does not yet know what month Cheryl named Alberta. Albert says his first phrase: “I don’t know when your birthday is, but I know that Bernard doesn’t know either.” 3) Bernard has already crossed out the dates "May 19" and "June 18" immediately, since Cheryl did not tell him the numbers 18 and 19. There are no more such numbers in other months. Bernard understands that since he was silent, Albert crossed out these dates "May 19" and "June 18" too, realizing that it was not them. Bernard saw that in June, after the deletion, there was only one date "June 17". Bernard knows that Sherrill has only given Albert a month. If Cheryl had called Alberta "June," Albert would have said he knew when her birthday was. It would be June 17th. But Albert said he didn't know when he said his first phrase. Bernard crosses out "June 17" at home. 4) Bernard looks at the dates, after which he says the phrase "At first I did not know, but now I know." We can conclude that Cheryl told him the number 17, which is in August, since there are no more non-repeating numbers and Bernard determined that her birthday is "August 17"! ! The problem has been solved in principle. But by condition it is not written that one must calculate the Birthday or both. 5) Confirmation of the answer. Albert crossed out the dates "May 19", "June 18", "June 17". Albert realizes that after his first sentence, Bernard crossed out "June 17" too, because he understands that Bernard understood after his words that the date is not June. He sees that the number 17 is still in another month of "August". After the phrase uttered by Bernard, he has no doubts that Cheryl's birthday is "August 17". Albert says his second phrase: "Great, now I know too." Cheryl's birthday is "August 17" !!