16 children are standing in line to receive a total of 100 pieces of candy, with each child guaranteed to receive at least 1 piece. At least how many pieces must the first child in line receive to ensure that he or she has the greatest number after all 100 pieces are distributed?

Hint: â€śat leastâ€ť.

give 8 choco to first child

rest are 7+7+(6+6+â€¦13 children)

first will still get highest number of chocolates

given answer is not 8

am i doing something wrong?

The question mentions at least 1 piece of candy each has to receive, which means each one can receive more than 1 candyâ€¦

So now if you distribute each one 1 candy (16 candies gone to 16 people)â€¦leftover candy = 100-16 = 84.

Now divide 84 by 2 = 42.

So if you distribute 42 to each oneâ€¦the second and the third person gets equal. Increase 1 for the 1st candidate and reduce 1 from the second person

The distribution is like this.

44 42 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Note that it is mentioned at least he should receive 44 candiesâ€¦(the second personâ€™s candies you can distribute amongst the 14â€¦whatever you do the value cannot exceed 44). I hope this helps. The concept is a bit esoteric I can say!

the first child has to be given minimum number of candies but he/she should have the highest candies right?(I think this is the question)

each child should receive atleast 1 implies we shouldnâ€™t leave any child without giving a candy this does not imply we cannot give more than 1

two criteria must be met

giving least number of candies and ensuring the first child to have the greatest number of candies compared to others

You are right thatâ€™s what I was trying to explain youâ€¦

But if you choose 8, (7), [7], 6, 6,â€¦

Notice that you can take 6 candies out of the second kid (highlighted within first braces) and give it to the third person [highlighted within third brackets] â€¦in that case your first criteria fails and the third person has 13 candiesâ€¦

That is the entire conceptâ€¦No matter what approach you select to distribute the answer will always be 44.

43 is the wrong answer.

case 0: 85,1,1,1

case 1 : 44,42,1,1,â€¦

case 2 : 8,7,7,6,6,â€¦

can you please explain which conditions case 2 violates?

sorry I donâ€™t seem to get your explanation.

I am saying case 1 and case 2 are two valid possibilities but case 2 is to the left most in the spectrum whereas case 0 is the right most in the spectrum. case 1 lies somewhere in between

doesnâ€™t case2 satisfy all the given conditions?

can you write the final distribution in your case ?

Thanks for rectifyingâ€¦I forgot to add the one that I had already distributed!..my bad!

The sixth student can have 9 candies.

Thank you.

â€śmustâ€ť is the key word.

What if 14 children get 6 each,(i.e. 84 total will be distributed already and leaving us with only 16 chocolates).15th one gets 7 chocolates and that then lefts us with the at least greatest one to be with just â€ś9â€ť.

what is wrong with this logic??

The question is framed in a way that it is our job to ensure that they have the greatest number **after all the 100 candies are distributed**(we have to just focus on how many candies the first child have and then no can else can have this number) .

The question is worded like this :

If we give 9 candies to the first child then no child shall have this amount of candies (we have no control over how much candies the rest of the children get except they have to be greater than 1), So the second child can also pick 9 candies or more(Your logic fails ).

Got it, thanks

16 children are standing in line to receive a total of 100 pieces of candy, with each child guaranteed to receive at least 1 piece. At least how many pieces must the first child in line receive to ensure that he or she has the greatest number after all 100 pieces are distributed?

For this question, Greg gives the answer as 44. However, since it is asked that the 1st child has to receive the greatest number, why canâ€™t it be 43? The 1st and the 2nd child both might receive 43 pieces and it still satisfies the required condition. Can someone clear my doubt?

It canâ€™t be 43 because if the 1st and the 2nd child both receive 43 pieces , it doesnâ€™t mean the 1st child has the greatest no. of candies since the second one has same no. of candies.

When solving this problem below, why canâ€™t the first child have 85 pieces, leaving the remaining 15 pieces of candy for the other 15 students (1 piece for each student)?

The question is asking â€śAt leastâ€ť, meaning what is the minimum number of candies that the person should take to have the largest.