Problem Solving

Three boxes of supplies have an average weight of 7 kg and a median weight of 9 kg. What is the maximum possible weight, in kg of the lightest box?
1
2
3
4
5

Ans given = 3

My ans = 1 Please help me understand where I am wrong.
Sum of 3 weights = 21
Median = 9 => sum of 1st and 3rd = 12
Given 1st <= 9 and Last >= 9
Max of Last = 11 => Least of First = 1 ?

Your mistake is that you taken the max value for the heaviest box.

We have to find the maximum possible weight of the smallest box.
In this case, 3, 9, 9 is a valid combination of values. Do you agree?
Another possible combination is 2,9,10. So 1 can never be the maximum possible value of the lightest box as we have already identified 2 combinations in which weight of the lightest box can be 2 or 3.

(a+b+c)/3=7, b=9,a<=b<=c

a+c=12, we only have three options

1+11
2+10
3+9

the maximum weight of the lightest is the highest value between the small values on the left