How to solve this candy boxes problem?

Ganesh Ujwal

New member
Aug 10, 2014
A boy has 10 boxes of candies with him, with an average of 18 candies per box. If each box has atleast 9 candies then what can be the max possible number of candies in any box?

I can only tell total number of candies that is 10 * 18 = 180.

Remaining I can't tell.


Full Member
Mar 25, 2016
Hm... well, let's carefully re-read the problem and see if we can't glean any more information from it.

...what [is] the max[imum] possible number of candies in any box?
Alright, so now we know the goal of the exercise. We want to find the maximum number of candies that can be in one of the boxes. Can you see why if we're maximizing one box, we must also be minimizing every other box?

If each box has at least 9 candies...
This is the other key piece of information we needed. This tells us the minimum number of candies that we can have. Putting these two things together, we now know we're going to have nine boxes with 9 candies each and one box with all the rest of the candies. You've correctly identified that in order for the average number of candies per box to be 18, there must be 180 candies in total... so how many candies must be in the maximized box?