Gone After Blackout

When Andy asked Beth if she had eaten more than him, Beth replied that she didn't know. We can deduce from this that Beth had eaten at least 2 candies because if she had eaten only one her response would have been "No". When Beth asked if Cici had eaten more than her, Cici replied that she didn't know. Since we know that Beth had at least two candies (and Cici knows this as well), then we can deduce that Cici ate at least 3 candies, otherwise she would have said "No".

At this point Dave knows for a certainty the exact distribution of candies. The only way for Dave to know the exact distribution is for him to have taken the maximum number of candies while everyone else took the minimum, namely {1,2,3,5}. If Dave had only taken 4, then there would be some uncertainty (it could have been {1,3,3,4} or {2,2,3,4}) and he couldn't have honestly known the exact distribution.

Andy=A Beth=B Cici=C Dave=D Lets ignore the first 4 candies eaten and add 1 to A, B, C and D at the end (for simplicity's sake) Clue 1. "Andy first asked Beth, "Did you eat more than I did?" Beth answered, "I don't know." "
Meaning B>=1 If Beth had eaten 0 then she would know for sure that she did not eat more than Andy (Andy cannot eat less than 0) Clue 2. "Then Beth asked Cici, "Did you eat more than I did?" Cici answered, "I don't know."" Meaning C>B: C>=2 Same logic as clue 1, Cici "is smart enough to catch the implications of the conversations" so she knows that Beth ate at least 1 candy. Therefore she ate at least 2 candies, if she ate less than 2 she would know for sure that she did not eat more than Beth. Clue 3. "Upon hearing these, Dave said he knew the exact distribution of the 11 candies." The only way for Dave to know the distribution for sure is if he had the maximum amount of candies possible and the others the minimum amount possible. If he ate 1 (or more) less than the maximum amount then he would not know for sure who that extra candy had gone to and would not know "the exact distribution". For Andy the minimum is 0, for Beth the minimum is 1, for Cici the minimum is 2, There are 4 left so Dave ate 4. Add 1 to each person (that we took off at the start) and you have A=1, B=2, C=3, D=5

firstly beth answered that "he did't know", that means he must have eaten 2 or more than two candies because if he had eaten 1 candy he must have said no.

then when cici answered beth, he answered the same as beth did and even he has also listened that beth has told to andy that he don' know , that means he have eaten 3 or more than three candies as beth has eaten 2 or more candies then he must have eaten 3 or more candies

You can set some boundary conditions, Andy, Beth, and Cici could not have taken more than three candies. Because had any of them taken more than three they would have known that no one else could have had more candy and thus Andy would have no reason to ask Beth if she had more candy, nor would would Beth or Cici follow up, since they would know of their majority take on the candies

now dave knows about distribution that means he has eaten most candies and therefore the answer is 1,2,3,5

(A IS ANDY, B IS BETH, C IS CICI AND D IS DAVE) IF B HAD EATEN LESS THAN A, HE WOULD HAVE SAID NO (BOTH ATE AT LEAST 1. B MUST HAVE CONSIDERED THE POSSIBILITY THAT A ATE 1 ONLY WHILE ANSWERING, SO HE HAVING EATEN MORE AND NOT WANTING TO ADMIT, SAID HE WAS NOT SURE. BECAUSE THERE IS ALSO A POSSIBILITY CONSIDERED BY B THAT A ATE MORE THAN 1 JUST LIKE HIM AND MAY BE MORE THAN HIM.) SO B ATE MORE THAN A. SIMILARLY C ATE MORE THAN B. NOW D WILL SURELY IN HIS SOLUTION NOT INDICATE THAT HE ATE ANY CANDY WHEN THE LIGHTS WERE OUT. SO WE TAKE D=1. NOW C>B>A>1. NOW NEGLECTING (ONLY FOR NOW) THE FIRST ONE EATEN BY THEM, WE GET A+B+C=7. AND A<B<C. SO OUT OF ALL THE OPTIONS THE ONLY ONE SATISFYING THIS CONDITION IS A=5,B=3,C=2,D=1. HENCE THE ANSWER. .

Don't know if this is an appropriate answer,please clarify that for me....

At first $A$ asked $B$ and $B$ said "I don't know"

So I thought "Okay, $B$ perhaps ate more than $A$ because he's like "I don't know.I didn't eat anything" "

I thought the same with $C$ too.... and then $D$ came out this way "Haha..I know the answer..."

If I assumed that $A<B<C$ and I will leave $D$ just out of the sum.

I came up with possibilities like * $(1,2,3,5)$ , $(1,2,4,4)$ * and many more.....

Sorry for giving such a pointless answer,just wanted to give out my views.....

Andy asked Beth if she ate more than him, so Andy probably didn't eat more during the blackout. Then Beth asked Cici, and both don't know who ate more, so both ate at least 1 more. Dave knew the distribution, so he is sure he ate more than anyone else.

Andy = 1+0, Dave = 1+4, Beth/Cici = 1+1 or 1+2 So, the solutions can be (1, 2, 3, 5) or (1, 3, 2, 5) and the one provided in the answers is (1,2,3,5)