Friday, November 14, 2008

புரிந்த புதிர்; புரிஞ்சதோட சரி. - 1

வணக்கம் மக்களே...

ஒரு விடுகதையோட உங்க முன்னாடி வந்திருக்கேன். இதுக்கு முடிஞ்சா பதில் கண்டுபிடிங்க. என்ன சந்தேகம் இருந்தாலும் கமெண்டுங்க. டிஸ்கஸ் பண்றாதா இருந்தாலும் கமெண்டுங்க. சரி இனி விடுகதைக்கு போவோம்.

மூனு பேரு வேல வெட்டி இல்லாம இருக்காங்க. A, B, C அப்டீனு வெச்சிக்குவோம்.

C என்ன பண்றான், 2ல இருந்து 100குள்ள ரெண்டு நம்பர மனசுல நெனச்சிக்கிறான். அந்த ரெண்டு நம்பர் X, Y அப்டீனு வெச்சிக்கலாம்.

C என்ன பண்றான்:
-- A கிட்ட போய், X+Y யோட விடைய சொல்றான்.
-- B கிட்ட போய், X*Y யோட விடைய சொல்றான்.

Aக்கு தெரிஞ்சது:
-- X+Y யோட விடை தெரியும்.
-- B கிட்ட X*Y யோட விடை இருக்குனு தெரியுமே தவிர, X*Y யோட விடை என்னான்னு தெரியாது.

Bக்கு தெரிஞ்சது:
-- X*Y யோட விடை தெரியும்.
-- A கிட்ட X+Y யோட விடை இருக்குனு தெரியுமே தவிர, X+Y யோட விடை என்னான்னு தெரியாது.

இது வரைக்கும் புரிஞ்சிதா? புரியலேனா go to step 1 :-) அட மறுபடியும் முதல்ல இருந்து படிங்கப்பா.

சரி இப்போ Aவும் Bயும் அந்த ரெண்டு நம்பர கண்டுப்புடிக்றாங்க. எப்படின்னா...
Statement 1: B கிட்ட A சொல்றான்: எனக்கு அந்த ரெண்டு நம்பரும் தெரில, உனக்குக் கூட கண்டிப்பா தெரியாதுனு எனக்குத் தெரியும்.
Statement 2:A கிட்ட B சொல்றான்: ஆமா, எனக்கு அந்த ரெண்டு நம்பர் முதல்ல தெரியாமத் தான் இருந்திச்சு. ஆனா, உன்னோட statement 1 கேட்டப் பிறகு, எனக்கு அந்த ரெண்டு நம்பர் தெரிஞ்சிப் போச்சு.
Statement 3: B கிட்ட A சொல்றான்: ஆஹா, உன்னோட இந்த statement 2 வ கேட்டுட்டப் பிறகு எனக்குக் கூட அந்த ரெண்டு நம்பர் தெரிஞ்சிப் போச்சு.

அப்படீனு சொல்றாங்க.

ஆக, X மற்றும் Y என்னான்னு கண்டு புடிங்க.

பி.கு1. A கிட்ட B பொய் சொன்னான். B கிட்ட A பொய் சொன்னான், அப்டீங்கற மொக்கைக்கெல்லாம் இங்குட்டு இடம் கிடையாது.
பி.கு.2 இந்த கேள்விக்கு பதில் என்கிட்டயும் இல்ல.

20 comments:

Anonymous said...

The numbers are 0 and 2.
X+Y is 2 the chances are it can be 1+1 or 0+2
so 1st person doesnot know the numbers
x*y is 0 it can be 0*(anything)

These (0,2) are the lowest 2 numbers possible

Anonymous said...

Since B was told the x*y is 0, B guessed the numbers are 0 and 2 and based on this A knows his numbers can be only 0 and 2 otherwise B cannot say for sure that he knows the numbers.

Raji said...

Aiyyo kanna ippove kattuthe

Truth said...

@Anonymous,

The numbers range between 2 to 100 and not between 0 to 100. Apologies for the incomplete information. I have updated the post as well.

MathuKrishna said...

I have asked about this to all of my friends, and of course, they too are bright(!!!)as me!!!
He he he!!
Have anyone found the answer??!!
(If you have found it, please post it guys, உங்களுக்குப் புண்ணியமாப் போகும்!)

Truth said...

@ராஜி,
fash wash பண்ணிட்டு, ஒரு காபியோட உக்கருங்க. :)

Truth said...

@MathuKrishna,

இல்ல சொல்ல மாட்டேன் :)
தெரிஞ்ச உடனே சொல்லிட்றேங்க :)
ஆனா, எனக்கு கோவில் கட்டுவீங்களா? ;)

Anonymous said...

Possible numbers A can get
4 = 2+2
5 = 2+3
6 = 4+2, 3+3
7 = 2+5,3+4
more than this there are too many combinations. Based on statement 1 - A could have got 6 0r 7

For B
4 = 2*2
6 = 3*2
8 = 4*2
9 = 3*3
10 = 5*2
12 = 4*3 or 6*2
more than this there are too many combinations

So A could have gotten 6 or 7 for statement 1 to be true.

for statement 2 from B to be true he should have gotten 12 otherwise if he got 8 or 9 (for A to get 6) he knows the numbers exactly.

X+Y is 7
X*Y is 12
so the numbers are 3 and 4.

நந்து f/o நிலா said...

எச்சூஸ்மி தெரியாம உள்ள வந்துட்டேன். இங்க வேற என்னமோ நடக்குது.

எஸ்ஸாகிக்கறேன்...

lovely. said...

one thing is clear....... veala vati illatha antha moonu paeru yaru nu kandupudichetean..( answer is out of question )
1. u,
2. me,
3. now who is reading this comment.

யோசிப்பவர் said...
This comment has been removed by the author.
யோசிப்பவர் said...

//X+Y is 7
X*Y is 12
so the numbers are 3 and 4.
//
I think this cant be the right answer.

Reason : Consider the puzzle from top to bottom. If X and Y are 3 and 4, the A will get the number 7, which has two combinations of numbers for the sum - (2,5)(3,4). He dont know which pair is the right one. At this point, if the (3,4) is the right set then its product is 12 and 12 has three factors(2*2*3), so that A can guess that B couldnt find the answer. But if (5,2) is the right set, then its product is 10, which have ONLY the same two factors 5 and 2. So if (5,2) is the right set then B can able to tell the numbers. But A is saying that B also cant guess the numbers. So it should not be the case for (3,4) also. If X and Y are 3 and 4, then at this point when A is not sure about which set is right, he cant make the statement 1.

Sorry for the English explanation. Will think and post the answer later(may be in two three days).

Anonymous said...

I think you are reading between lines.

A got 7
B got 12.

A makes the statement 1 that he couldnot find the numbers because it can be 4+3 or 5+2 . At this point A doesnt care about B. He is just trying to get a clue thats why he says B cannot guess the numbers too, if he thinks that B can guess the numbers he knows exactly his numbers are 5 and 2. And then B who got 12 says statement 2 that he couldnot get the numbers (because it could be 4*3 or 6*2) but because A couldnt get the numbers and thinks B cannot guess the numbers because it is not anything less than 12. So B knows the numbers are 3 and 4 so he says he initially didnt know the numbers but now he does because of statement1. Now A knows based on B's answer (that he couldnot get the number initially) that he didnt get anything less than 12 but 12. So he guesses the numbers should be 3 and 4.

There is a very very small ambiguity in the second part of the statement 1 , but I guess that is the trick of the puzzle.

I am open to any other solution. Please let me know your thoughts.

யோசிப்பவர் said...

Dear Anony(I dont know your name),
Firstly, I'm not reading between the line.

A's first statement is "I dont know the numbers. And I'm sure that you also dont know that(or cant guess)"

Be clear that A dont know the B's number. So he(A) has to consider B's Choices, only in the means of his own sets of numbers.

Here, "A" can be sure about "B"s state, only if each set of A, tends "B"s to more than one set.

But if A has 7, then one of its set(5,2) tends B to have 10(consideration by A) which have only one set of option for B. So that A cant be sure at B's state.

Thats what I wants to point out. I'm sure, that the way we are dealing this problem is right. But we have to extend the option little more further, to get the right answer.

Truth said...

Dealing with prime factors is the right direction. I think,
--> A and B must have two sets in his mind, with some uncertainity.
--> after listening to stmt 1, B must eliminate one of the sets, giving him the answer
--> And now, after listening to stmt 2, A should also eliminate the ambiguity.

Sorta on the right lines.

யோசிப்பவர் said...

Finally I got the answer(atleast the minimum one). Firstly I tell the answer and then I'll explain.

The two numners are 4 and 13. Their sum is 17 and product is 52.

Its clear that not a single set of sum could be a set of both prime numbers. Thats what I tried to explain in last comments.

So what is the minimum number, which can be a sum of two numbers, greater than 2, so that all of its sets non prime numbers(Lets call this as non prime sets). the minimum is 11. So lets assume A have the number 11. And consider all of its subsets. They are (2,9)(3,8)(4,7)(5,6). Now B can be able to find out the numbers, only after A's statement. So its clear that, the product sets have minimum of two sets of number. From A, B gets the clue that A' sets are "non prime sets". So ONLY ONE B's set should tends to only single set of non prime sets of A and so B would be sure that would be the right set. But here we have 18,24,28,30. I this case B has both options 18 and 28, which have only single "non prime sets of A". So B cant able to guess which one is right, at this point. So our first assumption is wrong, ie. A is having 11 is wrong.

So considering number which have the next non prime sets is 17. Consider A is having 17. Now A could derive the sets (2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9), which all are non prime sets. SO B could have one of these numbers -30 / 42 / 52 / 60 / 66 / 70 / 72 . At this Point A makes the statement and B is able to derive the numbers. Except 52 all other numbers have more than one non prime sets of sums. For example Consider B is having 60. 60 has five possiblities regarding product - (2*30)(3*20)(4*15)(5*12)(6*10). But (5+12=17),(3+20=23) both are non prime sets of sum. another example take B have 66, then options are (2,33)(3,22)(6,11) and both (2+33=35), (6+11=17) are non prime sets. So eliminating all these multiple non prime sets we have only 52. which has the product options (2*26) and (4,13). (2+26=28) have two prime sets of addition (5,23) & (11,17). So we can eliminate this 28. The other option is only (4+13=17) which is a non prime set of addition, it should be the right one. So 17 is the sum and 52 is the Product of the numbers. So the numbers are (4,13)


I'm not sure whether I've presented the answer in an understandable way.

யோசிப்பவர் said...

For further confusions regarding this puzzle, refer my scribblings on http://yosinga.googlepages.com/notepad

:-)

Truth said...

சரியான விடை. யோசிப்பவரே, கலக்கிடீங்க. :)

யோசிப்பவர் said...

My Brother got some more answers for this puzzle. Can you tell me, where did you get this puzzle(source)??

Truth said...

@yosippavar,

one of my team mates from Hong Kong gave me this question.