Video Explanation

Text Explanation

We start off with 100 candies, and we want to distribute them among 10 children. But we have some conditions: no two children can have the same number of candies, and all must have at least 1.

We want to know the maximum number of candies that one child could receive. This means we essentially want one child to get as many candies as is possible given the limitations above.

So, we start with 100 candies. Let’s start by satisfying our second condition, which is that all children must have at least 1 candy. Once we give all 10 children 1 candy, we have 90 remaining, because we just distributed 10.

But we can’t give the remaining 90 to the one child to maximize his share. We haven’t yet met our first condition, which is that each child receive a different number of candies. Right now, they all have 1 candy.

We can fix this by giving each child a different number of candies, but we can still maximize the number given to one student by using the smallest numbers possible, starting from 1 and moving upwards. Like so:

Child 1: 1 candy

Child 2: 2 candies

Child 3: 3 candies

Child 4: 4 candies

Child 5: 5 candies

And so on, until we find that child 9 has been given 9 candies. We now want to subtract all of the candies assigned to the first 9 children from our 100 candies, and give the rest to child 10. Like so:

100 – 9 – 8 – 7 – 6 – 5 – 4 – 3 – 2 – 1 = 55 candies

Therefore, the maximum number of candies that child 10 can receive is 55. The answer is (E).