I had not participated in it. Was it some open contest like Codeagon? I went through the problems, here are my observations/approach, please correct me if I am wrong:

Problem 1: Observe $$$B<=15$$$, so from $$$(B+1)!$$$ all the numbers will be divisible because they will have at least B as a common factor.

Problem 2: Find the diameter and then $$$\sum\dfrac{cnt_i*(cnt_i-1)}{2}$$$, where $$${cnt_i}$$$ is the count of nodes in the subtree of a child of the node which lies on the diameter.

Problem 3: You can do a knapsack kind of dp, $$$dp[i][j]$$$ denotes whether for the first $$$i$$$ elements, the sum $$$j$$$ is possible or not. Then iterate for $$$dp[n][j]$$$, for minimum $$$j$$$ which is possible, and subtract it from the total sum of bad luck mentioned in the problem to maximize it.