anitank: If they were all labelled incorrectly, the fewest number of marbles u can pick is TWO.

For those of you saying it's just one marble, if you choose a black marble B from the box labeled white W, how would you be sure since the box could contain all black marbles BB or black and white marbles BW

You will have to choose two marbles from the same box to ascertain the contents of the remaining boxes

VoodooDoll: Either two marbles or zero marbles if this is a trick question.

Two marbles to get a bw mixture in each box or zero marbles if a trick question that just involves relabelling the boxes.

MoyoGENERAL: pls mod/ guys, how can I edit the front page? is it not possible?

MissMeiya:

It expires after a certain amount of time. Next time don't abandon us for so long! Lol

tos4u: U will need to pick one box labeled as having 2 black marble. Pick d first mable and the second marble and see their color. U Wil then know the original label of dat box, then look for anoda box labeled as the color of the the 2 marbles u pick and exchange the label to the original u now found out then interchange then on the remainin two boxes without opening them,
So in conclusion u need to pick 2 marbles from any of d box to determine them.

MoyoGENERAL: yeeeeeehhhhhh
I can't believe I made FP
dancing all kind of dance.....
where was I?
I DON MISSSSSSS OOOOOOOO
MEN.......
Now to give you guys the answer......
the answer is one......yes, one
explanation:
practically get three bowls, put two black balls in one, two white balls in one and one black and one white in the other, then intentionally label the boxes wrongly....if ( box containing W W) labelled as B W, then (box containing BB) labelled as WW, and ( box containing BW) as BB....the question is what is the least possible marble you will pick to determine all three content....
guys if you pick from the box wrongly labelled as BW, let's say you pick W, you will know that That box will contain WW and BW since its wrongly labelled....this leaves you with the second box wrongly labelled to be interchanged to BB( since you know the 3rd box is wrongly labelled and we have established the first box as WW,) now the third box is BW...
pronto....

ChukChinCol:
I think ua wrong. Lets be practical. Let capital letter represent d label and smal letter d content eg WW (wb), BB (ww), WB (bb). Using ur formula: if i pick frm WB (wch actually has bb), u suggestd i pick both. As i find its bb, u suggest i look 4d label BB (wch contains ww) and interchange it.
Hello...?

deadie:

Please make sure that you know the correct answer to a puzzle before you post one. Your answer is wrong and I had already provided you with the correct answer. Here is your proof.

Based on the solution that you provided.
Box 1 contains WW, but is labeled BW (picked W and then conclude that it is WW since it is wrongly labeled)
Box 2 contains BB, but is labeled WW (you simply interchanged the remaining two labels).
Box 3 contains BW, but is labeled BB

Now tell me, will your solution work if:
Box 1 contains WW, but is labeled BB (picked W: no conclusion as to what this box contains. Could be either WW or BW. You can only conclude that it is not BB)
Box 2 contains BB, but is labeled BW (Could be BB, WW, or BW since you have not concluded on the contents of Box 1 and Box 3)
Box 3 contains BW, but is labeled WW (Could be BB, WW, or BW since you have not concluded on the contents of Box 1 and Box 2)

Your solution is therefore wrong. I have provided you with the solution earlier (Second page).

tos4u: My guy am 100 percent right, see wen u pick out d 2 black marble look for d label on anoda box and put it on d d box which contain d 2 black marble, den instead of puttin d first label on d one u latter remove, jus interrchange on the one u never removed d label and put tht label on d secon label u latter removed, withot opening d other boxes,
like i say u only need 2 marbles to determine them, thanks
Am a mathematicians so i advice u check my xplainatn again

MoyoGENERAL:

Puzzle 2...
this is a trickier one....

"Mrs Joy's five daughters each gave books for Christmas to one or more of her sisters. Each presented four books and each received four books, but no two girls allocated her book the same way. That is, only one gave two books to one sister and two to another. Beth gave all her books to Alice; Christy gave three to Edith; which sisters gave the four books to Deborah??

and again....you guys are allowed to cheat...lol
next question comes up when we have a correct answer...

lobell:

So, to avoid duplication in their distribution patterns this arrangement has to be followed. One sister gave all her books to one sister(4;0). The second sister gave three and one books respectively to two sisters(3;1). The third sister gave two and two books respectively to two sisters(2;2). The fourth sister must give two and one and one books respectively to three sisters(2;1;1) while the last sister can only give one and one and one and one books respectively to four sisters(1;1;1;1)!

EXPLANATION (edited)
Beth gave all four books to Alice
Christy gave three to Edith remaining one
Therefore the only combinations left for Deborah are:
She gets two books from one girl (Edith or Alice) and one each from two other girls (Christy (compulsorily), and Edith or Alice(depending on who gave her two)). QED

NOTE: Deborah must of necessity be the one who gave two books to one sister and her remaining two books to another sister!!!

MoyoGENERAL:

lobell:


So, one sister gave all her books to one sister. The second sister gave three and one books to two sisters. The third sister gave two and two books to two sisters. The fourth sister gave two and one and one books to three sisters while the last sister gave one and one and one and one books to four sisters!

EXPLANATION
Beth gave all four books to Alice
Christy gave three to Edith remaining one
Therefore the only combinations left for Deborah are:
She gets two books from one girl and one each from two other girls. QED

please make it clearer....
the question is which sisters gave the four books to Deborah?

MissMeiya:

Answer: Alice and Christie gave 1 book each and Edith gave 2 books to Deborah.

Whooo! I remember this kind of puzzle. They use these puzzles for law school aptitude tests.
You use a chart like this to solve it:

           + - - + - - + - - + - - + - - +
           |  A  |  B  |  C  |  D  |  E  |
+ - - - - -+ - - + - - + - - + - - + - - +
| Alice    |  ×  |  1  |  1  |  1  |  1  |
+ - - - - -+ - - + - - + - - + - - + - - +
| Beth     |  4  |  ×  |  ×  |  ×  |  ×  |
+ - - - - -+ - - + - - + - - + - - + - - +
| Christie |  ×  |  ×  |  ×  |  1  |  3  |
+ - - - - -+ - - + - - + - - + - - + - - +
| Deborah  |  ×  |  2  |  2  |  ×  |  ×  |
+ - - - - -+ - - + - - + - - + - - + - - +
| Edith    |  ×  |  1  |  1  |  2  |  ×  |
+ - - - - -+ - - + - - + - - + - - + - - +

Start with the given information:
• None of them gave books to themselves. (image)
• "Beth gave all her books to Alice", so Beth cannot give any more books to anyone else. Also, Alice cannot receive any more books from anyone else. (image)
• "Christy gave three to Edith" (image)

Now, we reason:
• There are five different ways for the 4 books to be given:
- 4 (already used by Beth)
- 3-1
- 2-2
- 2-1-1
- 1-1-1-1
• Only Alice has enough open spaces to give the 1-1-1-1 combination. Now Edith has reached the four books she was given. This means no one else gave her any more books. (image)
• Deborah only has space to give the following combinations: 4 (already used by Beth), 3-1 (only possible by Christie), and 2-2. So it must be 2-2. This means Christie's remaining book came from Edith. (image)
• Edith can only give the 2-1-1 combination (3-1 is only possible by Christie). So she must give Beth 2 books or 1 book. So Beth's remaining book must come from Edith. This means no one else gave Beth any more books. This means Christie gave her remaining book to Deborah. This means Deborah's remaining 2 books came from Edith. (image)

dukila: For us to solve dis we must make assumptions

for me, assuming deborah was d sister tht gave 2 books each to 2 sisters den
Alice = 1betty, 1christy nd 1deborah nd 1Edith
betty= 4 Alice
Christy= 1 Deborah nd 3Edith
Deborah= 2 betty nd 2 christy
Edith= 1 Betty, 1 Christy, 2 Deborah

therefore Alice, christy nd Edith gave books to deborah.

MOBBDEEP: You need to draw a problem solving table.
Using this table, the following facts emerge since there are NO exact same way of giving and addition of all rows or columns must be 4:

Deduced Fact #1~Alice was the only one who could give one each to all 4 sisters because she is the only one with 4 empty spaces to give. Others have only 3 or less spaces.
Meanwhile, she can't take from Christy, Beth nor Edith again since she has already gotten her complete 4 from Beth.

Deduced Fact #2 ~Edith was the only one who got 3 from Christy (from your statement) + 1 from Alice (from the deduced fact #1 above). Therefore, she can't get anything from Deborah,Beth (she has given all her 4 to Alice) nor herself. Hence, her 4 is complete.

Deduced Fact #3 ~ Since Edith & Alice can no longer take from both Deborah again (their received 4 is complete), therefore, Deborah only has 2 people to give i.e Beth & Christy.
Meanwhile, the sum must be 4 and it must not be 3 + 1 since your rule says no pattern of distribution/giving is the same. But Christy has already given 3 to Edith which meant she gave the remaining 1 to someone.
What it means invariably is that Deborah can only give 2 each to both Christy & Beth.

Deduced Fact #4 ~ Since all the 4 sisters had 1 each from Alice (from Deduced Fact #1), therefore both Christy & Beth now have 3 each (from the Deduced Fact # above).
Which means both need extra 1 each from Edith to complete their 4.
By way of deduction again, this implies that after giving Beth & Christy 1 each, Edith can only give her last 2 to Deborah, who so far has only gotten 1 from Alice.

Deduced Fact #5 ~ Now that Deborah has 3, her last one will definitely come from Christy who is the only one who has not completed the 4.

SUMMARY:
Beth gave all 4 to Alice& received 1 from Alice, 2 from Deborah & 1 from Edith.
Christy gave 3 to Edith & 1 to Deborah and got 1 from Alice, 2 from Deborah & 1 from Edith.
Deborah gave 2 each to Beth & Christy and got 1 from Alice, 1from Christy & 2 from Edith.
Edith gave 1 to Beth, 1 to Christy & 2 to Deborah while getting 3 from Christy & 1 from Alice.
Alice gave 1 each to all 4 sisters & got 4 from Beth.


Meanwhile, something tells me we should be able to apply Kramer's Rule of Matrices to solve this problem.
Mathematician in the house!!!, help please.

MissMeiya: [size=18pt]WE HAVE A NEW PUZZLE. No more answers for puzzle 1.[/size]

MoyoGENERAL:
Puzzle 2...
this is a trickier one....
"Mrs Joy's five daughters each gave books for Christmas
to one or more of her sisters. Each presented four
books and each received four books, but no two girls
allocated her book the same way. That is, only one gave
two books to one sister and two to another. Beth gave
all her books to Alice; Christy gave three to Edith; which
sisters gave the four books to Deborah ??
and again....you guys are allowed to cheat...lol
next question comes up when we have a correct
answer...

saintneo:


This question requires no mathematics......referring to the person calling for kramers rule. It needs no chart as well.

There are several possible solutions.

First Deborah can't receive a book from herself and she can't receive from Beth as well because she gave all her books to Alice.
Deborah must receive a book from Christy.

And, Deborah will receive one book from Alice and two from Edith OR one book from Edith and two from Alice.

MissMeiya:
This puzzle has only one solution.


How do you know this?


Again, how do you know this? You based this on an unproved assumption.


Logical proofs must give... proof. The OP even said answers must be explained.

The answer is less important than the reasoning.

Start with the given information, and use logic to PROVE the answer.

Christy must give a book to Deborah.

This eliminates the duplication of 2-1-1 formation of giving by both Alice and Edith;

consequently, either Alice or Edith can go for the 2-1-1 distribution formulae OR 1-1-1-1 distribution formulae.

0-1-1-1-1
4-0-0-0-0
0-0-0-1-3
0-2-2-0-0
0-1-1-2-0

MissMeiya: saintneo

Here's the problem with this: you started with the correct answer and tried to work backward. I'll show you the problems in your proof:


This hasn't been proved yet.She could have given her fourth book to Beth.


Christy could not give 2-1-1, because she gave 3 books to Edith.


This is not true. Edith CANNOT give 1 book to each sister. Why? Beth gave 4 books to Alice. Therefore, Alice cannot receive a book from Edith.


This is a copy of the logic chart I made, except it is not labeled...


My point is simply: logic puzzles always have a set of steps to solve them. Finding those steps will lead you to write a good proof.

saintneo:
Solution1
0-1-1-1-1
4-0-0-0-0
0-0-0-1-3
0-2-2-0-0
0-1-1-2-0

Solution2
0-1-1-2-0
4-0-0-0-0
0-0-0-1-3
0-2-2-0-0
0-1-1-1-1

Isn't solution2 possible? Kindly read my explanation again.

MissMeiya:

Sorry, it isn't. Here's why:
In your last row, you have Edith giving herself 1 book.

I have to apologize for my tone. Thank you for being nice and not getting annoyed with me

saintneo:

I am glad you pointed out my mistake there.....that was an oversight. I need to upgrade the parity-bit in my memory.

About your tone....lol. Lawyers....lol!

kramer:

You need permission from me to do that

MissMeiya:

I'm so embarrassed smh.

Parity-bit? An error detection joke... You're a coder!

saintneo:

Nope. An EE Engineer.

MissMeiya:


Good grief. The answer is one, from the box labeled BW. I wrote the proof very neatly and clearly. Read it here https://www.nairaland.com/1809786/believe-me-going-make-sweat/4#24649189

We have moved on to a new puzzle.

deadie:

Good grief?
WHAT IF YOU PICKED A BLACK MARBLE FROM A BOX LABELED WW? THEN TELL ME, THE CORRECT LABEL OF ALL THE BOXES!!!

MOBBDEEP:
Sir, I don't know how to apply the principle.
Just felt it could be of application.
Master !!!, are you one & can you be of help?

kramer:

Hmm young Obi Won, in order to know how to apply the principle you must look into your inner self and become one with the force ... Only then will you be realize the true powers of my principle...