Kivi capital | quant | rejected

Kivi capital came to our campus for quant developer role.
College (tier 1) IT branch
They did a intital shortlisting on the basis of resume out of 250 only 18 were selected to give OA. OA was from college labs the question asked were.

1. You are given three arrays A,B,C (each of lenght<=10^5) of varing length. You need to find the minimum value of (Ai-Bj)^2+(Bj-Ck)^2+(Ai-Ck)^2.
2. You are given two integers N,K. You need to find the number of ways to build a sequence of N-2 numbers such that no two adjacent elements are same. You are also provided that first number is 1 and last is K of the sequence.(1<=N<=10^5)
3. You are given an array A of n numbers and you also have q queries you need to find for each query if you can create the query number from the bitwise OR of any subsequence of the array A.
   (1<=n<=10^5 || 1<=q<=1e5)

Out of 18 candidates 5 were selected for interview

1st Round (DSA and puzzle)

1. You need to convert one prime number to another prime number. Given the conditon that you can change one digit of the to another in one step and the new number formed should also be a prime number.
2. You are given a number n. intitally you are at 0 index you need to find the number of combinations of steps there are such that you would remain at the index 0 only. In one step you can either move one step left, or one step right, or can stay at the same place. You can move outside n and 0.
3. This was a puzzle . There is drawer in which there are red as well as blue socks you take two socks out of the drawer and the given probability that the given two socks are red is 1/2 . you need find the minimum number of socks that should be present in the drawer that would make this probablity satisfy
   Ans = 4 (3 red 1 blue)

3 were selected for next round.

Round 2 (subjects and puzzle)
1.The interviewers asked me about thread parallelism and concurrency problem. They showed a code and asked me what ouptut be of that code.They also asked how could I make that code concurrent.
2.Consider a system with 3 processes that share 4 instances of the same resource type. Each process can request a maximum of K instances. Resources can be requested and releases only one at a time. The largest value of K that will always avoid deadlock is.
After this he asked me to generalized formula for P processes and R resources.

3. Puzzle - You are given a Cake you need to make K cuts on the cake. The slices made after cuts need not to be equal in size. We need to find the maximum Slices we can make after K cuts.

2 candidates were selected after final round I was not one of them.