1. Eigenvectors and Eigenvalues of a Matrix 
 Find the eigenvectors and eigenvalues of an n*n matrix with n on the diagonal and ones on every other entry.
2. Sorting a Deviated Sequence 
 Given a sorted sequence of length n where each element's position deviates by at most k (with k < n), suggest an algorithm to sort the sequence.
3. Nested List to Binary Tree Conversion and Merging 
 The first part of the question involves pre-order traversal of a binary tree. The second part is similar to LeetCode problem 617, 'Merge Two Binary Trees'. The challenge here is that you are not given a root node or a node definition, but rather a nested list that you need to convert into a tree structure before proceeding.
4. Black and White Chess 
 Given a series of moves for both players in a game of black and white chess, return the number of black and white pieces on the board.
5. Fancy Number 
 Given a number n, return all the numbers in the open interval (0, n) that, when converted to base-4, consist only of the digits 0 and 1.