210 chocolate max

since only 2 boxes can contain the same no of chocolates.. the sum will be

2 with 15 = 30
2 with 14= 28...
and so on till last 2 boxes with 12 chocolates...


summing this will results in 210

Problem:
Every box can contain a maximum of 15 chocolates. If no three boxes can contain the same number of chocolates, what is the maximum number of chocolates a person can carry using 20 boxes?

Solution:
To find the maximum number of chocolates a person can carry using 20 boxes, we need to consider the possible combinations of chocolates in the boxes.

Maximum Number of Boxes:
Since no three boxes can contain the same number of chocolates, we need to distribute the chocolates in a way that no three boxes have the same number. Let's consider the maximum number of boxes possible:

1. If we have 1 chocolate in each of the 20 boxes, we have a total of 20 chocolates.
2. If we have 2 chocolates in each of the 20 boxes, we have a total of 40 chocolates.
3. If we have 3 chocolates in each of the 20 boxes, we have a total of 60 chocolates.

Observation:
From the above observation, we can see that the maximum number of chocolates we can have is when we have 2 chocolates in each of the 20 boxes, which gives us a total of 40 chocolates.

Explanation:
If we have 2 chocolates in each of the 20 boxes, we ensure that no three boxes have the same number of chocolates. This is because if we distribute the chocolates in any other way, we will end up with at least three boxes having the same number of chocolates.

For example, if we have 3 chocolates in one box, 2 chocolates in another box, and 2 chocolates in the remaining 18 boxes, we will have three boxes with 2 chocolates each.

Therefore, the maximum number of chocolates a person can carry using 20 boxes is 40.

Answer:
The maximum number of chocolates a person can carry using 20 boxes is 40. Therefore, the correct option is b) 105.