Wednesday, November 17, 2010

દીકરીઓની ઉંમર કેટલી ?


ગયા અંકનો સવાલ: 


એક વસ્તીગણતરીકાર એક ઘેર જાય છે જ્યાં એક માણસ એની ત્રણ દીકરીઓ સાથે રહેતો હતો.વસ્તીગણતરીકાર : "તમારી દીકરીઓની ઉંમર કેટલી છે?" ( કોઈ છોકરીની ઉંમર એના પપ્પાને તો પુછાય ને !!) માણસ: "એમની ઉંમેરોનો ગુણાકાર ૭૨ છે, અને સરવાળો મારા ઘર નંબર જેટલો છે."
વસ્તીગણતરીકાર :"પણ એ પુરતી માહિતી નથી."
માણસ: "સારું, સૌથી મોટી દીકરીને ચોકલેટ બહુ ભાવે છે."
કહો જોઈએ વાંચકો, આ ભાઈની દીકરીઓની ઉંમર !!


જવાબ:

આ  કોયડો  છેક ૧૮૫૯મા લખાયેલ પુસ્તક 'ધ કમ્પેનિયન ફોર યુથ'માં થોડા ભિન્ન સ્વરૂપે સૌ પ્રથમ વખત લખાયેલ. પછી કેટલાય જુદા જુદા સ્વરૂપોથી આ કોયડો ખુબ પ્રચલિત બન્યો.  આ કોયડાનો સાચો જવાબ છે: દીકરીઓની ઉંમર હશે  ૩,૩,અને ૮ વર્ષ.

ચાલો જોઈએ કેવી રીતે મળશે આવા આંકડા જયારે કોયડામાં ખાસ કઈ માહિતી આપી હોય એવું લાગતું નથી.
પ્રથમ વાક્ય: ઉંમેરોનો ગુણાકાર ૭૨ છે, અને સરવાળો મારા ઘર નંબર જેટલો છે.
હવે ૭૨ના અવયવો છે ૧,૨,૩,૪,૬,૮,૯,૧૨,૧૮,૨૪,૩૬,૭૨  અને વસ્તીગણતરીકારને  એનો ઘર નંબર  જાણે છે.

હવે શક્ય ઉકેલો નીચે મુજબ મળી શકે.

ક્રમ
નાની દીકરી
વચ્ચેની દીકરી
મોટી દીકરી
ઘર નંબર
1
1
1
72
74
2
1
2
36
39
3
1
3
24
28
4
1
4
18
23
5
1
6
12
19
6
1
8
9
18
7
2
2
18
22
8
2
3
12
17
9
2
4
9
15
10
2
6
6
14
11
3
3
8
14
12
3
4
6
13


હવે બીજું વાક્ય: "પણ એ પુરતી માહિતી નથી"
 મતલબ  એના ઘર નંબર માટે વસ્તીગણતરીકારને એકથી વધુ જવાબો મળ્યા જેથી એમણે કહ્યું કે માહિતી પુરતી નથી. નહિ તો એમણે જવાબ આપી દીધો હોત. આવી શક્યતા માત્ર ઘર નંબર ૧૪ માટે જ છે. (ઉપરના ટેબલ પરથી )
એટલે હવે બાકી રહેતા શક્ય ઉકેલો:
10
2
6
6
14
11
3
3
8
14


ત્રીજું વાક્ય :  સૌથી મોટી દીકરીને ચોકલેટ બહુ ભાવે છે.
મતલબ મોટી દીકરી એક જ છે. ઉપરના શક્ય ઉકેલોમાંથી પ્રથમ ( નંબર ૧૦ ) ઉકેલમાં બે મોટી દીકરીઓ હોવાથી, એ શક્યતા ગણકારતા મળતો જવાબ બે દીકરીઓની ઉંમર  ૩ વરસની  અને મોટી દીકરીની ઉંમર ૮ વર્ષની છે!!


જવાબ આપનાર વાંચકો:
સંપૂર્ણ સાચો  જવાબ માત્ર નેહલ  શાહે (હિંમતનગર) આપ્યો. અને ડીમ્પલ જોશીએ સારો પ્રયત્ન કર્યો.

End Game
ત્રણ નાના બોક્સ છે. દરેક બોક્સમાં બે લખોટીઓ છે. કુલ છ લખોટીમાં ત્રણ કાળી અને ત્રણ સફેદ લખોટીઓ છે. દરેક બોક્સ પર એક લેબલ લગાડેલ છે. દરેક લેબલ પર સફેદ-સફેદ, સફેદ-કાળો, અથવા કાળો-કાળો લખેલ છે. પણ દરેક લેબલ ખોટું છે. દા.ત. કાળો-કાળો લખેલ લેબલવાળા બોક્સમાં એક પણ કાળી લખોટી નથી. ઓછામાં ઓછા બોક્સ ખોલીને સાચા લેબલ બનાવવાના છે.  કેટલા બોક્સ ખોલશો તમે  ?

જવાબ ક્યાં મોકલશો?
તમારો જવાબ અમને ઈ મેઈલ દ્વારા alpeshbhalala@gmail.com પર મોકલી શકો છો અથવા www.alpeshbhalala.com  પર કોમેન્ટ દ્વારા મૂકી શકો છો.

14 comments:

Dipali said...

Dear Alpeshbhai
possibilities of putting marbles in box with all the labels wrong is only two.


case 1

Boxes Marbles kept in w-w b-b
w-b w-w b-b w-b

case 2

Boxes Marbles kept in w-w w-b
w-b b-b b-b w-w

thus by opening only one box , we can say which marble combination is there in which box.


for example we open b-b box and we found w-b combination than it is first case and if we found w-w combination it is second condition.

so answer is only one box is required to be opened .

with regards,

Dipali Shah (Kapadvanj)

Anonymous said...

i can do it by opening just one box. i would open the box on which "black-white" is written. now as this label is wrong the balls in the box would be either both balck or both white. means there are 2 possibilities when we open that box which are as follows.
1) first possibility is both the balls would be black, in this case the label of "black-black" would be sticked on this box and the box on which the label is "white-white" the label of "black-white" will be sticked since the label of "w-w" is wrong there is atleast one black in that box and the label of "w-w" will be sticked on the third box.
2) the second possibility is that both the balls in the box are white than in this case the label of "w-w" is sticked on that box. now the box on which the label is "black-black" the label of "white-black" will be sticked because the label is wrong therefore it would contain at least one black ball. and the label of "b-b" will sticked on the third box.thank you
from FENIL MEHTA...
my e-mail id- fmehtaa1991@hotmail.com

Urvesh Devani said...

ANSWER:--->>> 1 BOX

we need to open only 1 box.

reason:
given that all labels are wrong
so all have 2 choices.

black,black->
1->white-white,
2->white-black
white,black->
1->black-black,
2->white-white
white,white->
1->black-black,
2->white-black

now if we open any 1 box....
1 choice for another box will already be canceled.As there are only 2 choices for every box and 3 boxes total, we'll get final position for every box.

Thank you.

Anonymous said...

Hello Sir,

Myself, Mikul Bharatkumar Soni from Maninagar, Ahmedabad.

The answer to your question related to the 3 Boxes containing 3 Black & 3 White marbles which was asked in the "Shatdal" on Wednesday,17th Nov' 2010.

The right answer is :

"There is no need to open any Box. Because it is mentioned that each label is wrong. So, the Black-Black label don't contain any Black Marbles. So, simply replace the Black-Black label with White-White label and vice-versa for white -White label."

So, from 3 boxes, Black-Black label will be replaced by White-White label and White-White label will be replaced by Black-Black label and remaining label of Black-White is correct.

Regards...
Mikul Bharatkumar Soni.
C/3 Shivam Appt,
Jagabhai Park, Rambaug,
Maninagar,
Ahmedabad-380008

Mikul Soni said...

Mikul Bharatkumar Soni from Maninagar, Ahmedabad.

The answer to your question related to the 3 Boxes containing 3 Black & 3 White marbles which was asked in the "Shatdal" on Wednesday,17th Nov' 2010.

The right answer is :

"There is no need to open any Box. Because it is mentioned that each label is wrong. So, the Black-Black label don't contain any Black Marbles. So, simply replace the Black-Black label with White-White label and White-White label with Black-Black label."

So, from 3 boxes, Black-Black label will be replaced by White-White label and White-White label will be replaced by Black-Black label and remaining label of Black-White is correct.

Purvesh said...

only 1 box has to open which is stickered mix as black + white...because if we open the same and we found white colour that means...other box labled white is havine black marbles and the another one labled black having mix marbles...

Ved said...

Hi,
i am Ved Patel from baroda.
T he answer is 2 boxes. We need to open 2 boxes.
Reason
There are total 6 marbles, 3 of white colours and 3 of black colours.
If we open 1st box and we get 2 marbles of black colour and 2 of different colours. Then, we naturally know that in the 3rd box the other marbles will be of white colours.
In this way we can make the correct labels by opening only 2 boxes.


i send an email to you with visuals

Ved said...

Hi,
i am Ved Patel from baroda.
The answer is 2 boxes. We need to open 2 boxes.
Reason
There are total 6 marbles, 3 of white colours and 3 of black colours.
If we open 1st box and we get 2 marbles of black colour and 2 of different colours. Then, we naturally know that in the 3rd box the other marbles will be of white colours.
In this way we can make the correct labels by opening only 2 boxes.


i send an email to you with visuals

Ved said...

we need to open only one box as you only said that there is not a single black marble in the box with label black-black.Then in this box both the marbles are white
open the other box if it both the marbles are black then in other box one will be white and other will be black.
in this way we can form correct label by opening one box only

Yatharth said...

It's very easy !!!
I will open only one box: WHITE - BLACK

nirvisha said...

As mentioned in the given problem, all labels are wrong and also explained that if black-black[BB] is written ,it does not contain a single black!marble[lakhoti] .Then, puzzle is wrong. As in that case "BB" label must be on box containing both "WW" marbles and the box labeleled as "WW" must contain both "BB". Then in that case label on box containing "W-B" must "w-B" which is correct label!!.but as per problem no box is marked correctly and only 3 labels exist.!

nirvisha

Rikin said...

my name is rikin shah.
we have to open only one box which had tag of black-white tag.
reason,,,,,,
if we open it we will get b-b marble or w-w marble, because tag is wrong.
now if we got b-b marble then w-w marble in black-black box and b-w marble in white-white box,because tag is wrong.
now if we got w-w marble in it then b-w marble in black-black box and b-b marble in white-white box.

Umang Galaiya said...

Hello. I am Umang Galaiya from Jamnagar. We need to open only one box and that is the Black-White one. Because, all the labels are wrong. And if we open the Black-White box, we can make out what coloured marbles are there in the other two boxes, because, ALL THE LABELS ARE WRONG!

RAVI - THE COOL BOY said...

right ans is 1 box

every label is wrong.
It means [W-W] labeled box doesn't contain both white marbles.
[W-B] labeled box doesn't contain white and black marbles. It means it contains either both black or both white marbles.
[B-B] labeled box doesn't contain both black marbles.


So there are two possibilities.



Possibilities Labeled Boxes
of wrong labels [W-W] [B-W] [B-B]
1 BB WW BW
2 BW BB WW


As example now If I open [W-W] box, I'll find either BB marbles or BW marbles.
If I find BB marbles, I'll understand that [B-W] box is containing either WW marbles or BW marbles.
But mentioned in the puzzle that every label is wrong, I'll understand that in [B-W] box there can't be BW marbles, but there must be the WW marbles. So in [B-B] labeled box there must be WW marbles.

Thus, We find where the marbles are.
Now we can change the labels.





Thus, just opening one box you can correct the labels.


Ravi Soni