Sheeps and Three sons
A guy is owner of a certain number of sheeps for god's sakes and also the father of three sons who for some reason are expert logicians. So here comes the question.Clever as you are will think to yourself, now all this guy needs is to believe he's about to die so that he can make a will to divide the sheeps among the sons, right? Right, Except He calls them together (the sons, not the sheeps) and tells them how many sheeps (not sons) he owns AND Adds that
1. The eldest will inherit the most sheeps
2. The youngest the least
3. Nobody having more than 10 sheeps, which as we all know is a crime.
4. He then whispers in each son's ear how many sheeps he personally will inherit.
After that he proceeds from the eldest to the youngest, asking each ALOUD if he can calculate how many sheeps each of his brothers will inherit and each replies, "NO". He does it again and again each replies, "No" But then the eldest son on being asked the question once more says, "Yes, each of the last two 'noes' (that's the plural of 'no') gave me some information, and I now know (no plural of 'knows') how many sheeps each of us will inherit." What's the bet you're already wondering how may sheeps each son will get?
QUESTION IS HOW MANY SHEEPS EACH ONE WILL GET ?
* NO POINTS WITHOUT EXPLAINATION
1. The eldest will inherit the most sheeps
2. The youngest the least
3. Nobody having more than 10 sheeps, which as we all know is a crime.
4. He then whispers in each son's ear how many sheeps he personally will inherit.
After that he proceeds from the eldest to the youngest, asking each ALOUD if he can calculate how many sheeps each of his brothers will inherit and each replies, "NO". He does it again and again each replies, "No" But then the eldest son on being asked the question once more says, "Yes, each of the last two 'noes' (that's the plural of 'no') gave me some information, and I now know (no plural of 'knows') how many sheeps each of us will inherit." What's the bet you're already wondering how may sheeps each son will get?
QUESTION IS HOW MANY SHEEPS EACH ONE WILL GET ?
* NO POINTS WITHOUT EXPLAINATION
Labels: friday special, puzzle
posted by Rajesh Lal at
9:57 PM
10 Comments:
This is a very tricky question. To get the correct answer I need to know how many times the question was asked.
Lets consider there are 11 sheeps and the possibilities are
E - Eldest, M - 2nd brother, Y - Youngest
1. E * 6 + M * 3 + Y * 2 = 11
2. E * 6 + M * 4 + Y * 1 = 11
3. E * 5 + M * 4 + Y * 2 = 11
4. E * 7 + M * 3 + Y * 1 = 11
These are the 4 most complex probabilities.
Say if father told his elder son that he will get 6, 2nd son will get 4 and Youngest will get 1.
When father told elder son that he will get 6 sheeps, M and Y could get 3 and 2 or 4 and 1 respectively.
Similarly when father told his 2nd son that he will get 4 sheeps, E and L could get 6 and 1 or 5 and 2 respectively.
Similarly when father told his Youngest son that he will get 1 sheeps, E and L could get 7 and 3 or 6 and 4 respectively.
So from the first question nobody will be able to give an answer. But when father asked his elder son again, and since the 3 brothers are expert logicians and couldn't answer the first question which means the 2nd son will get either 3 or 4 and youngest will get either 1 or 2 because any other number they could have easily guessed the correct answer.
Number of times this question was asked to everyone with an answer as 'NO' means there are those many possibilities for each of them.
So if there are 4 possibilities for the Elder brother with the number he was told, he will get the right answer when the same question is asked the 5th time.
--Jugs
Wow...I am NOT a mathmetician by a long shot so Jugs, you have certainly confused me. :)
By looking at the situation and the 4 guidelines the father had to go by, number 3 states that no person can have more than 10 sheep...so, let's say the dad could only have 10.
The simplest answer is as follows:
Oldest son = 4
Middle son = 3
Youngest son = 2
This would have given dad 9 sheep to begin with and while there are other options to choose from using 6-10 sheep, this one uses the most sheep possible for dad to own while making the division to the sons as even as possible and still following numbers 1 and 2 of the guidelines.
As for number 4 of the guidelines and the paragraph following it, I ignored it as extra, non-essential 'stuff'.
Well what the hell is the answer???
ANSWER
---------------------------
The sons get either 10, 6 and 3 sheeps each or 9, 7 and 3
GOT RIGHT
---------------------------
NO ONE
What's the explaination Rajesh???
the answer is 2,3,5.
first, from the 3rd point, we know that having more than 10 sheeps is a crime. so the guy can't own more than 10 sheeps.
the youngest has to have at most 2 because having at least 3 would make the 3 son's numbers add up to more than 10. so the following combinations will work. (take note that 0 can't be an answer as he is dividing the sheeps among the sons so that means the youngest has to have at least 1) the two younger sons can't have 1,2 respectively because the eldest son would be able to figure out the other 2 amounts. this is because the number of sheeps have been told to the 3 sons. so we are left with these combinations
1.1,3,4=8
there is a least number, so if the elder had 4 and was given that total was 8, he can deduce that the other 2 had 3 and 1. so this can't be a possibility.
2.1,3,5=9
same thing with this
3.1,3,6=10
same thing with this
4.1,4,5=10
5.2,3,4=9
this can't be true as the eldest would know that since the total is 9, and he had 4, that the other 2 would have 2 and 3.
6.2,3,5=10
so we are down to two
1,4,5=10
2,3,5=10
if the middle son knows he has 4, he knows that the eldest has to have at least 5 which means that the youngest has to have 1 to total 10.
the answer is 2,3,5.
Does anyone other than me also get the fact that the plural of "sheep" is SHEEP??
Eldest son will have 6 sheep, middle will have 3 sheep youngest will have 1 sheep. if its a crime to have more than 10 sheep the father cannot have more than 10.
The answer is unanswerable. I have worked out only 2 possibilities. They would melt your brain if you actually saw them. However, because of the dialog in posting, it is virturally impossible to tell. The reason why is because of the ranges that the 'Sheeps' could be distributed. The Master could have as little as 7 'Sheeps' or as much as 10. AND the little brother could have 0 'Sheeps' and still have the least. If it said "every brother will receive at least 1 'Sheeps' then I have worked out ONE answer. As it stands, there is a seemingly infinitessimal number of permutations of a single scenario.
Here is the solution I worked out: Read it through if you have the time.
Sheeps and Three sons
A guy is owner of a certain number of sheeps for god's sakes and also the father of three sons who for some reason are expert logicians. So here comes the question.Clever as you are will think to yourself, now all this guy needs is to believe he's about to die so that he can make a will to divide the sheeps among the sons, right? Right, Except He calls them together (the sons, not the sheeps) and tells them how many sheeps (not sons) he owns AND Adds that
1. The eldest will inherit the most sheeps
2. The youngest the least
3. Nobody having more than 10 sheeps, which as we all know is a crime.
4. He then whispers in each son's ear how many sheeps he personally will inherit.
After that he proceeds from the eldest to the youngest, asking each ALOUD if he can calculate how many sheeps each of his brothers will inherit and each replies, "NO". He does it again and again each replies, "No" But then the eldest son on being asked the question once more says, "Yes, each of the last two 'noes' (that's the plural of 'no') gave me some information, and I now know (no plural of 'knows') how many sheeps each of us will inherit." What's the bet you're already wondering how may sheeps each son will get?
QUESTION IS HOW MANY SHEEPS EACH ONE WILL GET ?
Explination: First in order to solve this, it is necessary to answer 4 seperate questions in methodology of RANGES, that are constantly re-defined based upon logic. Once those four questions are refined down to one possibility, you are left with your answer.
Question1: How many maximum sheep does the Master have?
Question2: How many sheep will the Eldest receive?
Question3: How many sheep will Malcom (in the middle) receive?
Question4: How many sheep will the Youngest receive?
Lets start with the Master. The Master cannot have more than 10 sheep, because that is against the Law. The Story also states that the Master has 'a certain number of sheeps' which is intended to be plural. Therefore he must have at least 2 sheeps. He also gives some to his eldest and another child, which by themselves is two sheep.
Therefore, Master(Ma), Eldest(El) Malcolm(Ml) and Youngest(Yg) can be defined as such:
Ma = 10 - 2
El = ?
Ml = ?
Yg = ?
Lets look at the rules a little bit. None of the sons know what the other son received the first go around, but they were told by the Master how many 'Sheeps' he has. Therefore, one can reason the following:
If the Youngest receives none, Malcolm receives 1 and the Eldest receives 2, then that makes 3 sheep that the Master has in inventory. If the Master says to his Eldest, Logician son that he has 3 'Sheeps' and he is to receive 2 of them, he can very easily predict that Malcolm would recieve 1 and the Youngest nothing based upon the rules givin. Therefore, the Master must have more than three 'Sheeps'.
Lets suppose that the Master has 4. Upon telling the Eldest (who could not work out the number of 'Sheeps' the first time around) that he has 4, and that the Eldest is to receive 2 of them, we reach a contradiction in that the Youngest doesn't receive the least. If the Eldest receives 3, then he CAN work out that he has three, Malcolm one, and the Youngest zero. If he has all four, then we reach a similar contradiction to the rules given before.
Lets, therefore, suppose that the Master has 5 'Sheeps'. The Eldest could have 3, Malcolm 2, and the Youngest 0. This is Workable. The Eldest could not have 4 or 5, because both create a contradiction that is either workable the first time around (the Eldest having known the Maximum number of 'Sheeps' and his total) or that the Youngest doesnot share the Least, but shares a number contiguous with Malcolm. The Eldest cannot have 2, because there is a surplus of distribution that would satisfy the ruling, where Malcolm shares the same number of 'Sheeps' with a brother.
Lets finally suppose the Master has 6 'Sheeps'. With 6, the Eldest could receive not receive 5, because he could work from Eldest to Youngest, 5, 1, 0. He could not receive 4, because he could work 4, 2, 0. He could not receive 3, because he could work 3, 2, 1. Therefore, the Master must have more than 6 'Sheeps'. This enables us to redefine the Master's number of 'Sheeps' according to the ruling as such:
Ma = 10 - 7
El = ?
Ml = ?
Yg = ?
With 7, as I'm sure, you have worked out, the Eldest could receive 4 'Sheeps' but would not know if Malcolm has 3 and the Youngest 0, or if Malcolm has 2 and the Youngest 1. If the Eldest has just 3, then we reacu an un-workable situation with a contradiction. Therefore the LEAST number of 'Sheeps' the Eldest can receive is 4. If the Master doesn't have 7, but indeed has 10, then The Eldest could receive 7 'Sheeps' and not know weather Malcolm received 3 'Sheeps', and the Youngest 0, or if Malcolm received 2, and the youngest 1. With the Eldest receiving 8 'Sheeps' it is unanimously workable that the Eldest would have 8, Malcolm 2, and the Youngest 0. Since the Eldest did not know how many 'Sheeps' his brothers had the first time around, we can reason that at the Maximum number of 'Sheeps' (10), the Eldest cannot recieve more than 7 'Sheeps' without being able to work out the remainder of his 'Sheeps' about his brothers, being a Master Logician. This allows us to re-define the following to as such:
Ma = 10 - 7
El = 7 - 4
Ml = ?
Yg = ?
En working with the Eldest's ranges, lets look at Malcolm in the Middle here. In order for Malcolm to be a valid recipiant of a 'certain number of Sheeps' he must receive at least one more 'Sheeps' than the Youngest and one less 'Sheeps' than the Eldest. We also know the range of the Eldest. Lets permutate some different scenarios. If the Eldest receives 7 'Sheeps' then that leaves 3 'Sheeps' to distribute without the Eldest knowing how many 'Sheeps' each brother received. Malcolm could receive 2, or all 3. Therefore, the least number of 'Sheeps' that Malcolm could receive without the Eldest being able to work out how many 'Sheeps' his brother received is 2. If the Eldest receives 4 'Sheeps' then the Master's 'certain number of Sheeps' to distribute MUST be 7. This means that Malcolm can receive again, 2 or 3 'Sheeps'. Otherwise, the Eldest could work out the distribution. However, if the Master's 'certain number of Sheeps' is 10, and the Eldest received either 6 or 5 'Sheeps', then Malcolm could receive 4, and the Youngest 0, or 4 and the Youngest 1 respectively to the 5 and 6. If the Eldest received 5 and Malcolm 5, there would be a contradiction. Therefore, having exhaustedly scanned all contengencies between the the Master's 'certain number of Sheeps' range, and the inability for the Eldest, who is a Master Logician to deterine the distribution of 'Sheeps' amungst his bretheren, we can re-define Malcolm in the Middle's range as such:
Ma = 10 - 7
El = 7 - 4
Ml = 4 - 2
Yg = ?
Now, turning to the Youngest, who also knows the Master's 'certain number of Sheeps, and how many 'Sheeps' he is to receive, we know that he recieves the least, which could be 0. Therefore, he cannot receive less than 0. The maximum permutation of scenario can be located in the above logical steps in that the Master has 10 'Sheeps', and the Eldest would receive 5. This means Malcolm could receive 3, and the Youngest 2. If the Eldest receives 6, then the numbers shy away out of favor for a maximum number of 'Sheeps' that the Youngest can receive. Therefore, the Youngest's 'certain number of Sheeps' that he will receive is between 2 and 0 as such:
Ma = 10 - 7
El = 7 - 4
Ml = 4 - 2
Yg = 2 - 0
We are left with 4 simplified permutations; The Master has 7, 8, 9, or 10 'certain number of Sheeps'. Lets take 7. If the Master has 7 'Sheeps' and tells the Eldest Logician that he will receive 4 'Sheeps', then the Eldest doesn't know if Malcolm will receive 2 and the Youngest 1, or if Malcolm will receive 3 and the Youngest 0. When the question is asked to Malcolm in the Middle, Malcolm at this point knows he will receive either 2 or 3. Malcolm, also being a Master Logician like his brothers, can reason that, if he would receive 2 then he knows that his Elder brother will receive more than him, being either 5 or 4 'Sheeps', leaving 1 or 0 'Sheeps' for his Younger brother. However, if he would receive 3 'Sheeps', he, also knowing the Master's 'certain number of Sheeps' being 7, that his Elder brother MUST have 4 (4 + his 3 = 7) and his Younger brother having 0. This is workable, yet his brother claims that he doesn't know. Therefore from this permutation, we reason that IF the Master has 7 'Sheeps' then Malcolm must receive 2 of them. This is as such:
Ma = 10 - 7
El = 7 - 4
Ml = 4 - 2
Yg = 2 - 0
Ma = 7, El = 4, Ml = 2, Yg = 1
Please note that if the Master has 7 'Sheeps' and tells his Eldest that he will receive anything other than 4 'Sheeps', then a contradiction apepars.
Lets explore the scenario of the Master having 8 'Sheeps'. The Eldest's range MUST be 5. Any other scenario between 0 and 8 creates multiple contradictions. With the Eldest knowing there are 8 'Sheeps' total, and that he would receive 5 'Sheeps', then he cannot know if Malcolm would receive 2 and the Youngest 1, or if Malcolm would receive 3 and the Youngest 0. Therefore, he would respond to the inquiry with "No". Malcolm, we know, would either know he is to receive 2 or 3 'Sheeps'. If Malcolm knows he is to receive 3 'Sheeps', he doesn't know weather the Eldest has 5, and the Youngest 0, or if the Eldest has 4, and the Youngest 1, as both scenarios are valid. If, however, Malcolm is to receive 2 'Sheeps', he will know that the Master's 'certain number of Sheeps' is 8 and that IF, the Eldest does not know what his brothers have, then he must be receiving 5 'Sheeps'. Otherwise, the Eldest would receive either 5 or 6 'Sheeps' (making 1 or 0 'Sheeps' for the Younger brother). If the Eldest receives 6 'Sheeps', then he would most assuredly know that there are 8 'certain number of Sheeps', and that his 6 'Sheeps' leaves 2 'Sheeps' to be distributed, and that Malcolm must have 2 'Sheeps' in order to maintain the Master's ruling. He, being a Master Logician would be able to work this out. Therefore, If the Master has 8 'certain number of Sheeps', then the following scenarious would be as such:
Ma = 10 - 7
El = 7 - 4
Ml = 4 - 2
Yg = 2 - 0
Ma = 7, El = 4, Ml = 2, Yg = 1
Ma = 8, El = 5, Ml = 2, Yg = 1
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