Interactive problems aren't very popular in coding contests because they involve additional effort from the problem writers. But they are usually pretty creative. I've made a shortlist below. Have fun solving them in the comments section!

# (CLRS, agora scholarships 2004) You are given two arrays A and B of n and m elements. The elements in each array are sorted and distinct. Find the kth element in the union of two arrays using as few comparisons as possible.

# (CLRS, agora scholarships finals 2004) You are given two arrays A and B of n and m elements. The elements in each array are sorted and distinct. Find the kth element in the union of two arrays using as few comparisons as possible.

# (CLRS, interview question) You are given a matrix A with n rows and m columns. The elements in each row and each column are distinct and sorted. One query is what’s the value of A[i][j]. Find out if element x is in the matrix using as few queries as possible.
# (CLRS, romanian national olympiad) Given an array A of n integers. Find the 2nd minimum in the array using as few comparisons as possible.
# (CLRS) Given an array A of n integers find out the minimum and maximum elements of the array using as few comparisons as possible.